(3x-1)(-4x-2)=0

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Solution for (3x-1)(-4x-2)=0 equation: 


Simplifying
(3x + -1)(-4x + -2) = 0

Reorder the terms:
(-1 + 3x)(-4x + -2) = 0

Reorder the terms:
(-1 + 3x)(-2 + -4x) = 0

Multiply (-1 + 3x) * (-2 + -4x)
(-1(-2 + -4x) + 3x * (-2 + -4x)) = 0
((-2 * -1 + -4x * -1) + 3x * (-2 + -4x)) = 0
((2 + 4x) + 3x * (-2 + -4x)) = 0
(2 + 4x + (-2 * 3x + -4x * 3x)) = 0
(2 + 4x + (-6x + -12x2)) = 0

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

Solving
2 + -2x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -1x + -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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