12(2x+7)(x-6)=0

Solution for 12(2x+7)(x-6)=0 equation:

Simplifying
12(2x + 7)(x + -6) = 0

Reorder the terms:
12(7 + 2x)(x + -6) = 0

Reorder the terms:
12(7 + 2x)(-6 + x) = 0

Multiply (7 + 2x) * (-6 + x)
12(7(-6 + x) + 2x * (-6 + x)) = 0
12((-6 * 7 + x * 7) + 2x * (-6 + x)) = 0
12((-42 + 7x) + 2x * (-6 + x)) = 0
12(-42 + 7x + (-6 * 2x + x * 2x)) = 0
12(-42 + 7x + (-12x + 2x2)) = 0

Combine like terms: 7x + -12x = -5x
12(-42 + -5x + 2x2) = 0
(-42 * 12 + -5x * 12 + 2x2 * 12) = 0
(-504 + -60x + 24x2) = 0

Solving
-504 + -60x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-42 + -5x + 2x2) = 0

Factor a trinomial.
12((-7 + -2x)(6 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3.5, 6}