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

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

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

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

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

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

Combine like terms: 3x + -12x = -9x
3(-18 + -9x + 2x2) = 0
(-18 * 3 + -9x * 3 + 2x2 * 3) = 0
(-54 + -27x + 6x2) = 0

Solving
-54 + -27x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -9x + 2x2) = 0

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

Ignore the factor 3.
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}