4(y+8)-2(y-5)=5(y-3)

Solution for 4(y+8)-2(y-5)=5(y-3) equation:

Simplifying
4(y + 8) + -2(y + -5) = 5(y + -3)

Reorder the terms:
4(8 + y) + -2(y + -5) = 5(y + -3)
(8 * 4 + y * 4) + -2(y + -5) = 5(y + -3)
(32 + 4y) + -2(y + -5) = 5(y + -3)

Reorder the terms:
32 + 4y + -2(-5 + y) = 5(y + -3)
32 + 4y + (-5 * -2 + y * -2) = 5(y + -3)
32 + 4y + (10 + -2y) = 5(y + -3)

Reorder the terms:
32 + 10 + 4y + -2y = 5(y + -3)

Combine like terms: 32 + 10 = 42
42 + 4y + -2y = 5(y + -3)

Combine like terms: 4y + -2y = 2y
42 + 2y = 5(y + -3)

Reorder the terms:
42 + 2y = 5(-3 + y)
42 + 2y = (-3 * 5 + y * 5)
42 + 2y = (-15 + 5y)

Solving
42 + 2y = -15 + 5y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-5y' to each side of the equation.
42 + 2y + -5y = -15 + 5y + -5y

Combine like terms: 2y + -5y = -3y
42 + -3y = -15 + 5y + -5y

Combine like terms: 5y + -5y = 0
42 + -3y = -15 + 0
42 + -3y = -15

Add '-42' to each side of the equation.
42 + -42 + -3y = -15 + -42

Combine like terms: 42 + -42 = 0
0 + -3y = -15 + -42
-3y = -15 + -42

Combine like terms: -15 + -42 = -57
-3y = -57

Divide each side by '-3'.
y = 19

Simplifying
y = 19