2(x-6)(2x+3)=0

Solution for 2(x-6)(2x+3)=0 equation:

Simplifying
2(x + -6)(2x + 3) = 0

Reorder the terms:
2(-6 + x)(2x + 3) = 0

Reorder the terms:
2(-6 + x)(3 + 2x) = 0

Multiply (-6 + x) * (3 + 2x)
2(-6(3 + 2x) + x(3 + 2x)) = 0
2((3 * -6 + 2x * -6) + x(3 + 2x)) = 0
2((-18 + -12x) + x(3 + 2x)) = 0
2(-18 + -12x + (3 * x + 2x * x)) = 0
2(-18 + -12x + (3x + 2x2)) = 0

Combine like terms: -12x + 3x = -9x
2(-18 + -9x + 2x2) = 0
(-18 * 2 + -9x * 2 + 2x2 * 2) = 0
(-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((-3 + -2x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-1.5, 6}