(3x+12)(7x+8)=0

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Solution for (3x+12)(7x+8)=0 equation: 


Simplifying
(3x + 12)(7x + 8) = 0

Reorder the terms:
(12 + 3x)(7x + 8) = 0

Reorder the terms:
(12 + 3x)(8 + 7x) = 0

Multiply (12 + 3x) * (8 + 7x)
(12(8 + 7x) + 3x * (8 + 7x)) = 0
((8 * 12 + 7x * 12) + 3x * (8 + 7x)) = 0
((96 + 84x) + 3x * (8 + 7x)) = 0
(96 + 84x + (8 * 3x + 7x * 3x)) = 0
(96 + 84x + (24x + 21x2)) = 0

Combine like terms: 84x + 24x = 108x
(96 + 108x + 21x2) = 0

Solving
96 + 108x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + 36x + 7x2) = 0

Factor a trinomial.
3((4 + x)(8 + 7x)) = 0

Ignore the factor 3.

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 '(8 + 7x)' equal to zero and attempt to solve:

Simplifying
8 + 7x = 0

Solving
8 + 7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7x = 0 + -8
7x = 0 + -8

Combine like terms: 0 + -8 = -8
7x = -8

Divide each side by '7'.
x = -1.142857143

Simplifying
x = -1.142857143
Solution
x = {-4, -1.142857143}

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