(2x^2-x)(2x+1)=0

Solution for (2x^2-x)(2x+1)=0 equation:

Simplifying
(2x2 + -1x)(2x + 1) = 0

Reorder the terms:
(-1x + 2x2)(2x + 1) = 0

Reorder the terms:
(-1x + 2x2)(1 + 2x) = 0

Multiply (-1x + 2x2) * (1 + 2x)
(-1x * (1 + 2x) + 2x2 * (1 + 2x)) = 0
((1 * -1x + 2x * -1x) + 2x2 * (1 + 2x)) = 0
((-1x + -2x2) + 2x2 * (1 + 2x)) = 0
(-1x + -2x2 + (1 * 2x2 + 2x * 2x2)) = 0
(-1x + -2x2 + (2x2 + 4x3)) = 0

Combine like terms: -2x2 + 2x2 = 0
(-1x + 0 + 4x3) = 0
(-1x + 4x3) = 0

Solving
-1x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 4x2) = 0

Factor a difference between two squares.
x((1 + 2x)(-1 + 2x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

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

Simplifying
x = -0.5
Subproblem 3
Set the factor '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

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

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -0.5, 0.5}