Solve for y 2(y-3)-6=-5(-4y+6)-6y

$2 (y - 3) - 6 = - 5 (- 4 y + 6) - 6 y$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 (- 4 y + 6) - 6 y = 2 (y - 3) - 6$

Step 2

Simplify $- 5 (- 4 y + 6) - 6 y$ .

Simplify each term.

Apply the distributive property.

$- 5 (- 4 y) - 5 \cdot 6 - 6 y = 2 (y - 3) - 6$

Multiply $- 4$ by $- 5$ .

$20 y - 5 \cdot 6 - 6 y = 2 (y - 3) - 6$

Multiply $- 5$ by $6$ .

$20 y - 30 - 6 y = 2 (y - 3) - 6$

Subtract $6 y$ from $20 y$ .

$14 y - 30 = 2 (y - 3) - 6$

Step 3

Simplify $2 (y - 3) - 6$ .

Simplify each term.

Apply the distributive property.

$14 y - 30 = 2 y + 2 \cdot - 3 - 6$

Multiply $2$ by $- 3$ .

$14 y - 30 = 2 y - 6 - 6$

Subtract $6$ from $- 6$ .

$14 y - 30 = 2 y - 12$

Step 4

Move all terms containing $y$ to the left side of the equation.

Subtract $2 y$ from both sides of the equation.

$14 y - 30 - 2 y = - 12$

Subtract $2 y$ from $14 y$ .

$12 y - 30 = - 12$

Step 5

Move all terms not containing $y$ to the right side of the equation.

Add $30$ to both sides of the equation.

$12 y = - 12 + 30$

Add $- 12$ and $30$ .

$12 y = 18$

Step 6

Divide each term in $12 y = 18$ by $12$ and simplify.

Divide each term in $12 y = 18$ by $12$ .

$\frac{12 y}{12} = \frac{18}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} = \frac{18}{12}$

Divide $y$ by $1$ .

$y = \frac{18}{12}$

Simplify the right side.

Cancel the common factor of $18$ and $12$ .

Factor $6$ out of $18$ .

$y = \frac{6 (3)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$y = \frac{6 \cdot 3}{6 \cdot 2}$

Cancel the common factor.

$y = \frac{6 \cdot 3}{6 \cdot 2}$

Rewrite the expression.

$y = \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{2}$

Decimal Form:

$y = 1.5$

Mixed Number Form:

$y = 1 \frac{1}{2}$

Solve for y 2(y-3)-6=-5(-4y+6)-6y

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