y^2-2y-2y+4=2y^2+y+8

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Solution for y^2-2y-2y+4=2y^2+y+8 equation: 


Simplifying
y2 + -2y + -2y + 4 = 2y2 + y + 8

Reorder the terms:
4 + -2y + -2y + y2 = 2y2 + y + 8

Combine like terms: -2y + -2y = -4y
4 + -4y + y2 = 2y2 + y + 8

Reorder the terms:
4 + -4y + y2 = 8 + y + 2y2

Solving
4 + -4y + y2 = 8 + y + 2y2

Solving for variable 'y'.

Reorder the terms:
4 + -8 + -4y + -1y + y2 + -2y2 = 8 + y + 2y2 + -8 + -1y + -2y2

Combine like terms: 4 + -8 = -4
-4 + -4y + -1y + y2 + -2y2 = 8 + y + 2y2 + -8 + -1y + -2y2

Combine like terms: -4y + -1y = -5y
-4 + -5y + y2 + -2y2 = 8 + y + 2y2 + -8 + -1y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-4 + -5y + -1y2 = 8 + y + 2y2 + -8 + -1y + -2y2

Reorder the terms:
-4 + -5y + -1y2 = 8 + -8 + y + -1y + 2y2 + -2y2

Combine like terms: 8 + -8 = 0
-4 + -5y + -1y2 = 0 + y + -1y + 2y2 + -2y2
-4 + -5y + -1y2 = y + -1y + 2y2 + -2y2

Combine like terms: y + -1y = 0
-4 + -5y + -1y2 = 0 + 2y2 + -2y2
-4 + -5y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-4 + -5y + -1y2 = 0

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

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

Ignore the factor -1.

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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

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

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