114=(5x+4)(3x-24)

Solution for 114=(5x+4)(3x-24) equation:

Simplifying
114 = (5x + 4)(3x + -24)

Reorder the terms:
114 = (4 + 5x)(3x + -24)

Reorder the terms:
114 = (4 + 5x)(-24 + 3x)

Multiply (4 + 5x) * (-24 + 3x)
114 = (4(-24 + 3x) + 5x * (-24 + 3x))
114 = ((-24 * 4 + 3x * 4) + 5x * (-24 + 3x))
114 = ((-96 + 12x) + 5x * (-24 + 3x))
114 = (-96 + 12x + (-24 * 5x + 3x * 5x))
114 = (-96 + 12x + (-120x + 15x2))

Combine like terms: 12x + -120x = -108x
114 = (-96 + -108x + 15x2)

Solving
114 = -96 + -108x + 15x2

Solving for variable 'x'.

Combine like terms: 114 + 96 = 210
210 + 108x + -15x2 = -96 + -108x + 15x2 + 96 + 108x + -15x2

Reorder the terms:
210 + 108x + -15x2 = -96 + 96 + -108x + 108x + 15x2 + -15x2

Combine like terms: -96 + 96 = 0
210 + 108x + -15x2 = 0 + -108x + 108x + 15x2 + -15x2
210 + 108x + -15x2 = -108x + 108x + 15x2 + -15x2

Combine like terms: -108x + 108x = 0
210 + 108x + -15x2 = 0 + 15x2 + -15x2
210 + 108x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
210 + 108x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(70 + 36x + -5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(70 + 36x + -5x2)' equal to zero and attempt to solve:

Simplifying
70 + 36x + -5x2 = 0

Solving
70 + 36x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-14 + -7.2x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7.2x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -7.2x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7.2x + x2 = 0 + 14
-7.2x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7.2x + x2 = 14

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = 14 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = 14 + 12.96

Combine like terms: 14 + 12.96 = 26.96
12.96 + -7.2x + x2 = 26.96

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 26.96

Calculate the square root of the right side: 5.192301994

Break this problem into two subproblems by setting 
(x + -3.6) equal to 5.192301994 and -5.192301994.

Subproblem 1
x + -3.6 = 5.192301994

Simplifying
x + -3.6 = 5.192301994

Reorder the terms:
-3.6 + x = 5.192301994

Solving
-3.6 + x = 5.192301994

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = 5.192301994 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = 5.192301994 + 3.6
x = 5.192301994 + 3.6

Combine like terms: 5.192301994 + 3.6 = 8.792301994
x = 8.792301994

Simplifying
x = 8.792301994

Subproblem 2
x + -3.6 = -5.192301994

Simplifying
x + -3.6 = -5.192301994

Reorder the terms:
-3.6 + x = -5.192301994

Solving
-3.6 + x = -5.192301994

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = -5.192301994 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = -5.192301994 + 3.6
x = -5.192301994 + 3.6

Combine like terms: -5.192301994 + 3.6 = -1.592301994
x = -1.592301994

Simplifying
x = -1.592301994

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.792301994, -1.592301994}
Solution
x = {8.792301994, -1.592301994}