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

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


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

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

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

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

Combine like terms: -6x + 4x = -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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