2y^2+2y-12=y^2-4y-12

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Solution for 2y^2+2y-12=y^2-4y-12 equation: 


Simplifying
2y2 + 2y + -12 = y2 + -4y + -12

Reorder the terms:
-12 + 2y + 2y2 = y2 + -4y + -12

Reorder the terms:
-12 + 2y + 2y2 = -12 + -4y + y2

Add '12' to each side of the equation.
-12 + 2y + 12 + 2y2 = -12 + -4y + 12 + y2

Reorder the terms:
-12 + 12 + 2y + 2y2 = -12 + -4y + 12 + y2

Combine like terms: -12 + 12 = 0
0 + 2y + 2y2 = -12 + -4y + 12 + y2
2y + 2y2 = -12 + -4y + 12 + y2

Reorder the terms:
2y + 2y2 = -12 + 12 + -4y + y2

Combine like terms: -12 + 12 = 0
2y + 2y2 = 0 + -4y + y2
2y + 2y2 = -4y + y2

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

Solving for variable 'y'.

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

Combine like terms: 2y + 4y = 6y
6y + 2y2 + -1y2 = -4y + y2 + 4y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
6y + 1y2 = -4y + y2 + 4y + -1y2

Reorder the terms:
6y + 1y2 = -4y + 4y + y2 + -1y2

Combine like terms: -4y + 4y = 0
6y + 1y2 = 0 + y2 + -1y2
6y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6y + 1y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(6 + y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {0, -6}

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