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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

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

Ignore the factor 2.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {1, 0.6666666667}

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