(3x-12)(4x+2)=0

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Solution for (3x-12)(4x+2)=0 equation: 


Simplifying
(3x + -12)(4x + 2) = 0

Reorder the terms:
(-12 + 3x)(4x + 2) = 0

Reorder the terms:
(-12 + 3x)(2 + 4x) = 0

Multiply (-12 + 3x) * (2 + 4x)
(-12(2 + 4x) + 3x * (2 + 4x)) = 0
((2 * -12 + 4x * -12) + 3x * (2 + 4x)) = 0
((-24 + -48x) + 3x * (2 + 4x)) = 0
(-24 + -48x + (2 * 3x + 4x * 3x)) = 0
(-24 + -48x + (6x + 12x2)) = 0

Combine like terms: -48x + 6x = -42x
(-24 + -42x + 12x2) = 0

Solving
-24 + -42x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -7x + 2x2) = 0

Factor a trinomial.
6((-1 + -2x)(4 + -1x)) = 0

Ignore the factor 6.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.5, 4}

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