(-6x+2)(4x-2)=0

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Solution for (-6x+2)(4x-2)=0 equation: 


Simplifying
(-6x + 2)(4x + -2) = 0

Reorder the terms:
(2 + -6x)(4x + -2) = 0

Reorder the terms:
(2 + -6x)(-2 + 4x) = 0

Multiply (2 + -6x) * (-2 + 4x)
(2(-2 + 4x) + -6x * (-2 + 4x)) = 0
((-2 * 2 + 4x * 2) + -6x * (-2 + 4x)) = 0
((-4 + 8x) + -6x * (-2 + 4x)) = 0
(-4 + 8x + (-2 * -6x + 4x * -6x)) = 0
(-4 + 8x + (12x + -24x2)) = 0

Combine like terms: 8x + 12x = 20x
(-4 + 20x + -24x2) = 0

Solving
-4 + 20x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5x + -6x2) = 0

Factor a trinomial.
4((-1 + 2x)(1 + -3x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0.5, 0.3333333333}

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