Solve for b 1/2*(2b-6)=2b

$\frac{1}{2} \cdot (2 b - 6) = 2 b$

Step 1

Simplify $\frac{1}{2} \cdot (2 b - 6)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (2 b - 6) = 2 b$

Simplify by adding zeros.

$\frac{1}{2} \cdot (2 b - 6) = 2 b$

Apply the distributive property.

$\frac{1}{2} (2 b) + \frac{1}{2} \cdot - 6 = 2 b$

Cancel the common factor of $2$ .

Factor $2$ out of $2 b$ .

$\frac{1}{2} (2 (b)) + \frac{1}{2} \cdot - 6 = 2 b$

Cancel the common factor.

$\frac{1}{2} (2 b) + \frac{1}{2} \cdot - 6 = 2 b$

Rewrite the expression.

$b + \frac{1}{2} \cdot - 6 = 2 b$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$b + \frac{1}{2} \cdot (2 (- 3)) = 2 b$

Cancel the common factor.

$b + \frac{1}{2} \cdot (2 \cdot - 3) = 2 b$

Rewrite the expression.

$b - 3 = 2 b$

Step 2

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

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

$b - 3 - 2 b = 0$

Subtract $2 b$ from $b$ .

$- b - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$- b = 3$

Step 4

Divide each term in $- b = 3$ by $- 1$ and simplify.

Divide each term in $- b = 3$ by $- 1$ .

$\frac{- b}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{3}{- 1}$

Divide $b$ by $1$ .

$b = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$b = - 3$