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

Ignore the factor 6.

Subproblem 1
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

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 = {-4, 0.5}

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