Solve for y 3*(12yi)=27+36i

$3 \cdot (12 y i) = 27 + 36 i$

Step 1

Simplify.

Multiply $12$ by $3$ .

$36 \cdot (y i) = 27 + 36 i$

Remove parentheses.

$36 \cdot y i = 27 + 36 i$

Step 2

Divide each term in $(36 \cdot (y i)) = 27 + 36 i$ by $36 i$ and simplify.

Divide each term in $(36 \cdot (y i)) = 27 + 36 i$ by $36 i$ .

$\frac{(36 \cdot (y i))}{36 i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Simplify the left side.

Multiply the numerator and denominator of $\frac{(36 \cdot (y i))}{36 i}$ by the conjugate of $36 i$ to make the denominator real.

$\frac{(36 \cdot (y i))}{36 i} \cdot \frac{i}{i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Multiply.

Combine.

$\frac{(36 \cdot (y i)) i}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Simplify the numerator.

Multiply $36 y i i$ .

Raise $i$ to the power of $1$ .

$\frac{36 y (i^{1} i)}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Raise $i$ to the power of $1$ .

$\frac{36 y (i^{1} i^{1})}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{36 y i^{1 + 1}}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Add $1$ and $1$ .

$\frac{36 y i^{2}}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{36 y \cdot - 1}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Multiply $- 1$ by $36$ .

$\frac{- 36 y}{36 i i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Simplify the denominator.

Add parentheses.

$\frac{- 36 y}{36 (i i)} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Raise $i$ to the power of $1$ .

$\frac{- 36 y}{36 (i^{1} i)} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Raise $i$ to the power of $1$ .

$\frac{- 36 y}{36 (i^{1} i^{1})} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 36 y}{36 i^{1 + 1}} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Add $1$ and $1$ .

$\frac{- 36 y}{36 i^{2}} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 36 y}{36 \cdot - 1} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Cancel the common factor of $- 36$ and $36$ .

Factor $36$ out of $- 36 y$ .

$\frac{36 (- y)}{36 \cdot - 1} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Move the negative one from the denominator of $\frac{- y}{- 1}$ .

$- 1 \cdot (- y) = \frac{27}{36 i} + \frac{36 i}{36 i}$

Rewrite $- 1 \cdot (- y)$ as $- (- y)$ .

$- (- y) = \frac{27}{36 i} + \frac{36 i}{36 i}$

Multiply $- (- y)$ .

Multiply $- 1$ by $- 1$ .

$1 y = \frac{27}{36 i} + \frac{36 i}{36 i}$

Multiply $y$ by $1$ .

$y = \frac{27}{36 i} + \frac{36 i}{36 i}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $27$ and $36$ .

Factor $9$ out of $27$ .

$y = \frac{9 (3)}{36 i} + \frac{36 i}{36 i}$

Cancel the common factors.

Factor $9$ out of $36 i$ .

$y = \frac{9 (3)}{9 (4 i)} + \frac{36 i}{36 i}$

Cancel the common factor.

$y = \frac{9 \cdot 3}{9 (4 i)} + \frac{36 i}{36 i}$

Rewrite the expression.

$y = \frac{3}{4 i} + \frac{36 i}{36 i}$

Multiply the numerator and denominator of $\frac{3}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$y = \frac{3}{4 i} \cdot \frac{i}{i} + \frac{36 i}{36 i}$

Multiply.

Combine.

$y = \frac{3 i}{4 i i} + \frac{36 i}{36 i}$

Simplify the denominator.

Add parentheses.

$y = \frac{3 i}{4 (i i)} + \frac{36 i}{36 i}$

Raise $i$ to the power of $1$ .

$y = \frac{3 i}{4 (i^{1} i)} + \frac{36 i}{36 i}$

Raise $i$ to the power of $1$ .

$y = \frac{3 i}{4 (i^{1} i^{1})} + \frac{36 i}{36 i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{3 i}{4 i^{1 + 1}} + \frac{36 i}{36 i}$

Add $1$ and $1$ .

$y = \frac{3 i}{4 i^{2}} + \frac{36 i}{36 i}$

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{3 i}{4 \cdot - 1} + \frac{36 i}{36 i}$

Multiply $4$ by $- 1$ .

$y = \frac{3 i}{- 4} + \frac{36 i}{36 i}$

Move the negative in front of the fraction.

$y = - \frac{3 i}{4} + \frac{36 i}{36 i}$

Cancel the common factor of $36$ .

Cancel the common factor.

$y = - \frac{3 i}{4} + \frac{36 i}{36 i}$

Rewrite the expression.

$y = - \frac{3 i}{4} + \frac{i}{i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$y = - \frac{3 i}{4} + \frac{i}{i}$

Rewrite the expression.

$y = - \frac{3 i}{4} + 1$

Reorder $- \frac{3 i}{4}$ and $1$ .

$y = 1 - \frac{3 i}{4}$

Solve for y 3*(12yi)=27+36i

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