-2y(y-4)=20-2y-12

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Solution for -2y(y-4)=20-2y-12 equation: 


Simplifying
-2y(y + -4) = 20 + -2y + -12

Reorder the terms:
-2y(-4 + y) = 20 + -2y + -12
(-4 * -2y + y * -2y) = 20 + -2y + -12
(8y + -2y2) = 20 + -2y + -12

Reorder the terms:
8y + -2y2 = 20 + -12 + -2y

Combine like terms: 20 + -12 = 8
8y + -2y2 = 8 + -2y

Solving
8y + -2y2 = 8 + -2y

Solving for variable 'y'.

Reorder the terms:
-8 + 8y + 2y + -2y2 = 8 + -2y + -8 + 2y

Combine like terms: 8y + 2y = 10y
-8 + 10y + -2y2 = 8 + -2y + -8 + 2y

Reorder the terms:
-8 + 10y + -2y2 = 8 + -8 + -2y + 2y

Combine like terms: 8 + -8 = 0
-8 + 10y + -2y2 = 0 + -2y + 2y
-8 + 10y + -2y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-8 + 10y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 5y + -1y2) = 0

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

Ignore the factor 2.

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

Simplifying
-4 + y = 0

Solving
-4 + y = 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 + y = 0 + 4

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

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

Simplifying
y = 4

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {4, 1}

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