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

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


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

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

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

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

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

Solving
-48 + -12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -2x + x2) = 0

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

Ignore the factor 6.

Subproblem 1
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

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 = {-2, 4}

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