(2x^3-3x^2)(-2x+3)=0

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


Simplifying
(2x3 + -3x2)(-2x + 3) = 0

Reorder the terms:
(-3x2 + 2x3)(-2x + 3) = 0

Reorder the terms:
(-3x2 + 2x3)(3 + -2x) = 0

Multiply (-3x2 + 2x3) * (3 + -2x)
(-3x2 * (3 + -2x) + 2x3 * (3 + -2x)) = 0
((3 * -3x2 + -2x * -3x2) + 2x3 * (3 + -2x)) = 0
((-9x2 + 6x3) + 2x3 * (3 + -2x)) = 0
(-9x2 + 6x3 + (3 * 2x3 + -2x * 2x3)) = 0
(-9x2 + 6x3 + (6x3 + -4x4)) = 0

Combine like terms: 6x3 + 6x3 = 12x3
(-9x2 + 12x3 + -4x4) = 0

Solving
-9x2 + 12x3 + -4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + 12x + -4x2) = 0

Factor a trinomial.
x2((-3 + 2x)(3 + -2x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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 '(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
Solution
x = {0, 1.5, 1.5}

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