3x^2-36x-75-108=0

Solution for 3x^2-36x-75-108=0 equation:

Simplifying
3x2 + -36x + -75 + -108 = 0

Reorder the terms:
-75 + -108 + -36x + 3x2 = 0

Combine like terms: -75 + -108 = -183
-183 + -36x + 3x2 = 0

Solving
-183 + -36x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-61 + -12x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-61 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-61 + -12x + x2 = 0

Solving
-61 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + -12x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + -12x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -12x + x2 = 0 + 61
-12x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
-12x + x2 = 61

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 = 61 + 36

Reorder the terms:
36 + -12x + x2 = 61 + 36

Combine like terms: 61 + 36 = 97
36 + -12x + x2 = 97

Factor a perfect square on the left side:
(x + -6)(x + -6) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -6) equal to 9.848857802 and -9.848857802.

Subproblem 1
x + -6 = 9.848857802

Simplifying
x + -6 = 9.848857802

Reorder the terms:
-6 + x = 9.848857802

Solving
-6 + x = 9.848857802

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 = 9.848857802 + 6

Combine like terms: -6 + 6 = 0
0 + x = 9.848857802 + 6
x = 9.848857802 + 6

Combine like terms: 9.848857802 + 6 = 15.848857802
x = 15.848857802

Simplifying
x = 15.848857802

Subproblem 2
x + -6 = -9.848857802

Simplifying
x + -6 = -9.848857802

Reorder the terms:
-6 + x = -9.848857802

Solving
-6 + x = -9.848857802

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 = -9.848857802 + 6

Combine like terms: -6 + 6 = 0
0 + x = -9.848857802 + 6
x = -9.848857802 + 6

Combine like terms: -9.848857802 + 6 = -3.848857802
x = -3.848857802

Simplifying
x = -3.848857802

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.848857802, -3.848857802}
Solution
x = {15.848857802, -3.848857802}