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

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


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

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

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

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

Combine like terms: -3x + -4x = -7x
x(6 + -7x + 2x2) = 0
(6 * x + -7x * x + 2x2 * x) = 0
(6x + -7x2 + 2x3) = 0

Solving
6x + -7x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -7x + 2x2) = 0

Factor a trinomial.
x((3 + -2x)(2 + -1x)) = 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 '(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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 1.5, 2}

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