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

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

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

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

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

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

Combine like terms: -6x + 24x = 18x
(-36 + 18x + 4x2) = 0

Solving
-36 + 18x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9x + 2x2) = 0

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-6, 1.5}