6(4x^2+18x-36)=0

Solution for 6(4x^2+18x-36)=0 equation:

Simplifying
6(4x2 + 18x + -36) = 0

Reorder the terms:
6(-36 + 18x + 4x2) = 0
(-36 * 6 + 18x * 6 + 4x2 * 6) = 0
(-216 + 108x + 24x2) = 0

Solving
-216 + 108x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-18 + 9x + 2x2) = 0

Factor a trinomial.
12((-6 + -1x)(3 + -2x)) = 0

Ignore the factor 12.
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}