Solve for y -3=12y-5(2y-7)

$- 3 = 12 y - 5 (2 y - 7)$

Step 1

Rewrite the equation as $12 y - 5 (2 y - 7) = - 3$ .

$12 y - 5 (2 y - 7) = - 3$

Step 2

Simplify $12 y - 5 (2 y - 7)$ .

Simplify each term.

Apply the distributive property.

$12 y - 5 (2 y) - 5 \cdot - 7 = - 3$

Multiply $2$ by $- 5$ .

$12 y - 10 y - 5 \cdot - 7 = - 3$

Multiply $- 5$ by $- 7$ .

$12 y - 10 y + 35 = - 3$

Subtract $10 y$ from $12 y$ .

$2 y + 35 = - 3$

Step 3

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

Subtract $35$ from both sides of the equation.

$2 y = - 3 - 35$

Subtract $35$ from $- 3$ .

$2 y = - 38$

Step 4

Divide each term in $2 y = - 38$ by $2$ and simplify.

Divide each term in $2 y = - 38$ by $2$ .

$\frac{2 y}{2} = \frac{- 38}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 38}{2}$

Divide $y$ by $1$ .

$y = \frac{- 38}{2}$

Simplify the right side.

Divide $- 38$ by $2$ .

$y = - 19$