y^3-y(2y-1)=

Solution for y^3-y(2y-1)= equation:

Simplifying
y3 + -1y(2y + -1) = 0

Reorder the terms:
y3 + -1y(-1 + 2y) = 0
y3 + (-1 * -1y + 2y * -1y) = 0
y3 + (1y + -2y2) = 0

Reorder the terms:
1y + -2y2 + y3 = 0

Solving
1y + -2y2 + y3 = 0

Solving for variable 'y'.

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

Factor a trinomial.
y((1 + -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 '(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 '(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, 1, 1}