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

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


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

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

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

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

Solving for variable 'y'.

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

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

Combine like terms: y2 + -2y2 = -1y2
-10y + -1y2 = 8y + 2y2 + -8y + -2y2

Reorder the terms:
-10y + -1y2 = 8y + -8y + 2y2 + -2y2

Combine like terms: 8y + -8y = 0
-10y + -1y2 = 0 + 2y2 + -2y2
-10y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1y'.
-1y(10 + y) = 0

Ignore the factor -1.

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

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10
Solution
y = {0, -10}

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