y^3-2y^2=3y

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

Simplifying
y3 + -2y2 = 3y

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

Solving
-2y2 + y3 = 3y

Solving for variable 'y'.

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

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

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

Factor a trinomial.
y((-1 + -1y)(3 + -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 + -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
Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {0, -1, 3}