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((-3 + -1y)(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 '(-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
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, -3, 1}