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

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

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

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

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

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

Combine like terms: -2x + 18x = 16x
2(-12 + 16x + 3x2) = 0
(-12 * 2 + 16x * 2 + 3x2 * 2) = 0
(-24 + 32x + 6x2) = 0

Solving
-24 + 32x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 16x + 3x2) = 0

Factor a trinomial.
2((-6 + -1x)(2 + -3x)) = 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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-6, 0.6666666667}