-2x(2x-3)(x-1)=0

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Solution for -2x(2x-3)(x-1)=0 equation: 


Simplifying
-2x(2x + -3)(x + -1) = 0

Reorder the terms:
-2x(-3 + 2x)(x + -1) = 0

Reorder the terms:
-2x(-3 + 2x)(-1 + x) = 0

Multiply (-3 + 2x) * (-1 + x)
-2x(-3(-1 + x) + 2x * (-1 + x)) = 0
-2x((-1 * -3 + x * -3) + 2x * (-1 + x)) = 0
-2x((3 + -3x) + 2x * (-1 + x)) = 0
-2x(3 + -3x + (-1 * 2x + x * 2x)) = 0
-2x(3 + -3x + (-2x + 2x2)) = 0

Combine like terms: -3x + -2x = -5x
-2x(3 + -5x + 2x2) = 0
(3 * -2x + -5x * -2x + 2x2 * -2x) = 0
(-6x + 10x2 + -4x3) = 0

Solving
-6x + 10x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 5x + -2x2) = 0

Factor a trinomial.
2x((-3 + 2x)(1 + -1x)) = 0

Ignore the factor 2.

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 '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1.5, 1}

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