(3x+12)(6x+7)=0

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Solution for (3x+12)(6x+7)=0 equation: 


Simplifying
(3x + 12)(6x + 7) = 0

Reorder the terms:
(12 + 3x)(6x + 7) = 0

Reorder the terms:
(12 + 3x)(7 + 6x) = 0

Multiply (12 + 3x) * (7 + 6x)
(12(7 + 6x) + 3x * (7 + 6x)) = 0
((7 * 12 + 6x * 12) + 3x * (7 + 6x)) = 0
((84 + 72x) + 3x * (7 + 6x)) = 0
(84 + 72x + (7 * 3x + 6x * 3x)) = 0
(84 + 72x + (21x + 18x2)) = 0

Combine like terms: 72x + 21x = 93x
(84 + 93x + 18x2) = 0

Solving
84 + 93x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + 31x + 6x2) = 0

Factor a trinomial.
3((4 + x)(7 + 6x)) = 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 '(7 + 6x)' equal to zero and attempt to solve:

Simplifying
7 + 6x = 0

Solving
7 + 6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = 0 + -7
6x = 0 + -7

Combine like terms: 0 + -7 = -7
6x = -7

Divide each side by '6'.
x = -1.166666667

Simplifying
x = -1.166666667
Solution
x = {-4, -1.166666667}

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