2y^3-y^2=2y^2+2y

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Solution for 2y^3-y^2=2y^2+2y equation: 


Simplifying
2y3 + -1y2 = 2y2 + 2y

Reorder the terms:
-1y2 + 2y3 = 2y2 + 2y

Reorder the terms:
-1y2 + 2y3 = 2y + 2y2

Solving
-1y2 + 2y3 = 2y + 2y2

Solving for variable 'y'.

Reorder the terms:
-2y + -1y2 + -2y2 + 2y3 = 2y + 2y2 + -2y + -2y2

Combine like terms: -1y2 + -2y2 = -3y2
-2y + -3y2 + 2y3 = 2y + 2y2 + -2y + -2y2

Reorder the terms:
-2y + -3y2 + 2y3 = 2y + -2y + 2y2 + -2y2

Combine like terms: 2y + -2y = 0
-2y + -3y2 + 2y3 = 0 + 2y2 + -2y2
-2y + -3y2 + 2y3 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-2y + -3y2 + 2y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-2 + -3y + 2y2) = 0

Factor a trinomial.
y((-1 + -2y)(2 + -1y)) = 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 '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

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

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

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5

Subproblem 3
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 = {0, -0.5, 2}

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