15(y-8)+15y-2y(y-8)=0

Solution for 15(y-8)+15y-2y(y-8)=0 equation:

Simplifying
15(y + -8) + 15y + -2y(y + -8) = 0

Reorder the terms:
15(-8 + y) + 15y + -2y(y + -8) = 0
(-8 * 15 + y * 15) + 15y + -2y(y + -8) = 0
(-120 + 15y) + 15y + -2y(y + -8) = 0

Reorder the terms:
-120 + 15y + 15y + -2y(-8 + y) = 0
-120 + 15y + 15y + (-8 * -2y + y * -2y) = 0
-120 + 15y + 15y + (16y + -2y2) = 0

Combine like terms: 15y + 15y = 30y
-120 + 30y + 16y + -2y2 = 0

Combine like terms: 30y + 16y = 46y
-120 + 46y + -2y2 = 0

Solving
-120 + 46y + -2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 23y + -1y2) = 0

Factor a trinomial.
2((-20 + y)(3 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + y)' equal to zero and attempt to solve:

Simplifying
-20 + y = 0

Solving
-20 + y = 0

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

Add '20' to each side of the equation.
-20 + 20 + y = 0 + 20

Combine like terms: -20 + 20 = 0
0 + y = 0 + 20
y = 0 + 20

Combine like terms: 0 + 20 = 20
y = 20

Simplifying
y = 20
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {20, 3}