(12x-3)(x+6)=

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

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

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

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

Multiply (-3 + 12x) * (6 + x)
(-3(6 + x) + 12x * (6 + x)) = 0
((6 * -3 + x * -3) + 12x * (6 + x)) = 0
((-18 + -3x) + 12x * (6 + x)) = 0
(-18 + -3x + (6 * 12x + x * 12x)) = 0
(-18 + -3x + (72x + 12x2)) = 0

Combine like terms: -3x + 72x = 69x
(-18 + 69x + 12x2) = 0

Solving
-18 + 69x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 23x + 4x2) = 0

Factor a trinomial.
3((-6 + -1x)(1 + -4x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-6, 0.25}