(x+3)(2x-12)=0

Solution for (x+3)(2x-12)=0 equation:

Simplifying
(x + 3)(2x + -12) = 0

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

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

Multiply (3 + x) * (-12 + 2x)
(3(-12 + 2x) + x(-12 + 2x)) = 0
((-12 * 3 + 2x * 3) + x(-12 + 2x)) = 0
((-36 + 6x) + x(-12 + 2x)) = 0
(-36 + 6x + (-12 * x + 2x * x)) = 0
(-36 + 6x + (-12x + 2x2)) = 0

Combine like terms: 6x + -12x = -6x
(-36 + -6x + 2x2) = 0

Solving
-36 + -6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(6 + -1x)) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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, 6}