2y^3-2y^2=3y^3-5y^2+2y

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Solution for 2y^3-2y^2=3y^3-5y^2+2y equation: 


Simplifying
2y3 + -2y2 = 3y3 + -5y2 + 2y

Reorder the terms:
-2y2 + 2y3 = 3y3 + -5y2 + 2y

Reorder the terms:
-2y2 + 2y3 = 2y + -5y2 + 3y3

Solving
-2y2 + 2y3 = 2y + -5y2 + 3y3

Solving for variable 'y'.

Reorder the terms:
-2y + -2y2 + 5y2 + 2y3 + -3y3 = 2y + -5y2 + 3y3 + -2y + 5y2 + -3y3

Combine like terms: -2y2 + 5y2 = 3y2
-2y + 3y2 + 2y3 + -3y3 = 2y + -5y2 + 3y3 + -2y + 5y2 + -3y3

Combine like terms: 2y3 + -3y3 = -1y3
-2y + 3y2 + -1y3 = 2y + -5y2 + 3y3 + -2y + 5y2 + -3y3

Reorder the terms:
-2y + 3y2 + -1y3 = 2y + -2y + -5y2 + 5y2 + 3y3 + -3y3

Combine like terms: 2y + -2y = 0
-2y + 3y2 + -1y3 = 0 + -5y2 + 5y2 + 3y3 + -3y3
-2y + 3y2 + -1y3 = -5y2 + 5y2 + 3y3 + -3y3

Combine like terms: -5y2 + 5y2 = 0
-2y + 3y2 + -1y3 = 0 + 3y3 + -3y3
-2y + 3y2 + -1y3 = 3y3 + -3y3

Combine like terms: 3y3 + -3y3 = 0
-2y + 3y2 + -1y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-2 + 3y + -1y2) = 0

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

Simplifying
-2 + y = 0

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

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

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

Simplifying
y = 2

Subproblem 3
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 = {0, 2, 1}

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