(3x+12)(4x+8)=0

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Solution for (3x+12)(4x+8)=0 equation: 


Simplifying
(3x + 12)(4x + 8) = 0

Reorder the terms:
(12 + 3x)(4x + 8) = 0

Reorder the terms:
(12 + 3x)(8 + 4x) = 0

Multiply (12 + 3x) * (8 + 4x)
(12(8 + 4x) + 3x * (8 + 4x)) = 0
((8 * 12 + 4x * 12) + 3x * (8 + 4x)) = 0
((96 + 48x) + 3x * (8 + 4x)) = 0
(96 + 48x + (8 * 3x + 4x * 3x)) = 0
(96 + 48x + (24x + 12x2)) = 0

Combine like terms: 48x + 24x = 72x
(96 + 72x + 12x2) = 0

Solving
96 + 72x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(8 + 6x + x2) = 0

Factor a trinomial.
12((4 + x)(2 + x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-4, -2}

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