Solve for y 4(4y-3)-(y-5)=-52

$4 (4 y - 3) - (y - 5) = - 52$

Step 1

Simplify $4 (4 y - 3) - (y - 5)$ .

Simplify each term.

Apply the distributive property.

$4 (4 y) + 4 \cdot - 3 - (y - 5) = - 52$

Multiply $4$ by $4$ .

$16 y + 4 \cdot - 3 - (y - 5) = - 52$

Multiply $4$ by $- 3$ .

$16 y - 12 - (y - 5) = - 52$

Apply the distributive property.

$16 y - 12 - y - - 5 = - 52$

Multiply $- 1$ by $- 5$ .

$16 y - 12 - y + 5 = - 52$

Simplify by adding terms.

Subtract $y$ from $16 y$ .

$15 y - 12 + 5 = - 52$

Add $- 12$ and $5$ .

$15 y - 7 = - 52$

Step 2

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

Add $7$ to both sides of the equation.

$15 y = - 52 + 7$

Add $- 52$ and $7$ .

$15 y = - 45$

Step 3

Divide each term in $15 y = - 45$ by $15$ and simplify.

Divide each term in $15 y = - 45$ by $15$ .

$\frac{15 y}{15} = \frac{- 45}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 45}{15}$

Divide $y$ by $1$ .

$y = \frac{- 45}{15}$

Simplify the right side.

Divide $- 45$ by $15$ .

$y = - 3$