(-6x+2)(-2x+1)=0

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Solution for (-6x+2)(-2x+1)=0 equation: 


Simplifying
(-6x + 2)(-2x + 1) = 0

Reorder the terms:
(2 + -6x)(-2x + 1) = 0

Reorder the terms:
(2 + -6x)(1 + -2x) = 0

Multiply (2 + -6x) * (1 + -2x)
(2(1 + -2x) + -6x * (1 + -2x)) = 0
((1 * 2 + -2x * 2) + -6x * (1 + -2x)) = 0
((2 + -4x) + -6x * (1 + -2x)) = 0
(2 + -4x + (1 * -6x + -2x * -6x)) = 0
(2 + -4x + (-6x + 12x2)) = 0

Combine like terms: -4x + -6x = -10x
(2 + -10x + 12x2) = 0

Solving
2 + -10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -5x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {0.3333333333, 0.5}

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