8x^2+36x-168=0

Solution for 8x^2+36x-168=0 equation:

Simplifying
8x2 + 36x + -168 = 0

Reorder the terms:
-168 + 36x + 8x2 = 0

Solving
-168 + 36x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + 9x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-42 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-42 + 9x + 2x2 = 0

Solving
-42 + 9x + 2x2 = 0

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

Divide each side by '2'.
-21 + 4.5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 4.5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 4.5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 4.5x + x2 = 0 + 21
4.5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
4.5x + x2 = 21

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 21 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 21 + 5.0625

Combine like terms: 21 + 5.0625 = 26.0625
5.0625 + 4.5x + x2 = 26.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 26.0625

Calculate the square root of the right side: 5.105144464

Break this problem into two subproblems by setting 
(x + 2.25) equal to 5.105144464 and -5.105144464.

Subproblem 1
x + 2.25 = 5.105144464

Simplifying
x + 2.25 = 5.105144464

Reorder the terms:
2.25 + x = 5.105144464

Solving
2.25 + x = 5.105144464

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 5.105144464 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 5.105144464 + -2.25
x = 5.105144464 + -2.25

Combine like terms: 5.105144464 + -2.25 = 2.855144464
x = 2.855144464

Simplifying
x = 2.855144464

Subproblem 2
x + 2.25 = -5.105144464

Simplifying
x + 2.25 = -5.105144464

Reorder the terms:
2.25 + x = -5.105144464

Solving
2.25 + x = -5.105144464

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -5.105144464 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -5.105144464 + -2.25
x = -5.105144464 + -2.25

Combine like terms: -5.105144464 + -2.25 = -7.355144464
x = -7.355144464

Simplifying
x = -7.355144464

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.855144464, -7.355144464}
Solution
x = {2.855144464, -7.355144464}