(4x-12)(6x+3)=0

Solution for (4x-12)(6x+3)=0 equation:

Simplifying
(4x + -12)(6x + 3) = 0

Reorder the terms:
(-12 + 4x)(6x + 3) = 0

Reorder the terms:
(-12 + 4x)(3 + 6x) = 0

Multiply (-12 + 4x) * (3 + 6x)
(-12(3 + 6x) + 4x * (3 + 6x)) = 0
((3 * -12 + 6x * -12) + 4x * (3 + 6x)) = 0
((-36 + -72x) + 4x * (3 + 6x)) = 0
(-36 + -72x + (3 * 4x + 6x * 4x)) = 0
(-36 + -72x + (12x + 24x2)) = 0

Combine like terms: -72x + 12x = -60x
(-36 + -60x + 24x2) = 0

Solving
-36 + -60x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + -5x + 2x2) = 0

Factor a trinomial.
12((-1 + -2x)(3 + -1x)) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
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
Solution
x = {-0.5, 3}