(6x-15)(x+8)=168

Solution for (6x-15)(x+8)=168 equation:

Simplifying
(6x + -15)(x + 8) = 168

Reorder the terms:
(-15 + 6x)(x + 8) = 168

Reorder the terms:
(-15 + 6x)(8 + x) = 168

Multiply (-15 + 6x) * (8 + x)
(-15(8 + x) + 6x * (8 + x)) = 168
((8 * -15 + x * -15) + 6x * (8 + x)) = 168
((-120 + -15x) + 6x * (8 + x)) = 168
(-120 + -15x + (8 * 6x + x * 6x)) = 168
(-120 + -15x + (48x + 6x2)) = 168

Combine like terms: -15x + 48x = 33x
(-120 + 33x + 6x2) = 168

Solving
-120 + 33x + 6x2 = 168

Solving for variable 'x'.

Reorder the terms:
-120 + -168 + 33x + 6x2 = 168 + -168

Combine like terms: -120 + -168 = -288
-288 + 33x + 6x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-288 + 33x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-96 + 11x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-96 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-96 + 11x + 2x2 = 0

Solving
-96 + 11x + 2x2 = 0

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

Divide each side by '2'.
-48 + 5.5x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 5.5x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 5.5x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 5.5x + x2 = 0 + 48
5.5x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
5.5x + x2 = 48

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 48 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 48 + 7.5625

Combine like terms: 48 + 7.5625 = 55.5625
7.5625 + 5.5x + x2 = 55.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 55.5625

Calculate the square root of the right side: 7.454025758

Break this problem into two subproblems by setting 
(x + 2.75) equal to 7.454025758 and -7.454025758.

Subproblem 1
x + 2.75 = 7.454025758

Simplifying
x + 2.75 = 7.454025758

Reorder the terms:
2.75 + x = 7.454025758

Solving
2.75 + x = 7.454025758

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 7.454025758 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 7.454025758 + -2.75
x = 7.454025758 + -2.75

Combine like terms: 7.454025758 + -2.75 = 4.704025758
x = 4.704025758

Simplifying
x = 4.704025758

Subproblem 2
x + 2.75 = -7.454025758

Simplifying
x + 2.75 = -7.454025758

Reorder the terms:
2.75 + x = -7.454025758

Solving
2.75 + x = -7.454025758

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -7.454025758 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -7.454025758 + -2.75
x = -7.454025758 + -2.75

Combine like terms: -7.454025758 + -2.75 = -10.204025758
x = -10.204025758

Simplifying
x = -10.204025758

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.704025758, -10.204025758}
Solution
x = {4.704025758, -10.204025758}