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

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


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

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

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

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

Combine like terms: -12x + 2x = -10x
(-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 + -3x)(2 + -1x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.3333333333, 2}

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