-3x(x-12)=18

Solution for -3x(x-12)=18 equation:

Simplifying
-3x(x + -12) = 18

Reorder the terms:
-3x(-12 + x) = 18
(-12 * -3x + x * -3x) = 18
(36x + -3x2) = 18

Solving
36x + -3x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 36x + -3x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 36x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 12x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 12x + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + 12x + -1x2 = 0

Solving
-6 + 12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -12x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -12x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -12x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -12x + x2 = 0 + -6
-12x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-12x + x2 = -6

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -6 + 36

Reorder the terms:
36 + -12x + x2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + -12x + x2 = 30

Factor a perfect square on the left side:
(x + -6)(x + -6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -6) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + -6 = 5.477225575

Simplifying
x + -6 = 5.477225575

Reorder the terms:
-6 + x = 5.477225575

Solving
-6 + x = 5.477225575

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.477225575 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.477225575 + 6
x = 5.477225575 + 6

Combine like terms: 5.477225575 + 6 = 11.477225575
x = 11.477225575

Simplifying
x = 11.477225575

Subproblem 2
x + -6 = -5.477225575

Simplifying
x + -6 = -5.477225575

Reorder the terms:
-6 + x = -5.477225575

Solving
-6 + x = -5.477225575

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.477225575 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.477225575 + 6
x = -5.477225575 + 6

Combine like terms: -5.477225575 + 6 = 0.522774425
x = 0.522774425

Simplifying
x = 0.522774425

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.477225575, 0.522774425}
Solution
x = {11.477225575, 0.522774425}