(-2+2y)y+3(-2+2y)=10

Solution for (-2+2y)y+3(-2+2y)=10 equation:

Simplifying
(-2 + 2y) * y + 3(-2 + 2y) = 10

Reorder the terms for easier multiplication:
y(-2 + 2y) + 3(-2 + 2y) = 10
(-2 * y + 2y * y) + 3(-2 + 2y) = 10
(-2y + 2y2) + 3(-2 + 2y) = 10
-2y + 2y2 + (-2 * 3 + 2y * 3) = 10
-2y + 2y2 + (-6 + 6y) = 10

Reorder the terms:
-6 + -2y + 6y + 2y2 = 10

Combine like terms: -2y + 6y = 4y
-6 + 4y + 2y2 = 10

Solving
-6 + 4y + 2y2 = 10

Solving for variable 'y'.

Reorder the terms:
-6 + -10 + 4y + 2y2 = 10 + -10

Combine like terms: -6 + -10 = -16
-16 + 4y + 2y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-16 + 4y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 2y + y2) = 0

Factor a trinomial.
2((-4 + -1y)(2 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-4, 2}