(2x-7)(-4x+18)=-24x+100

Solution for (2x-7)(-4x+18)=-24x+100 equation:

Simplifying
(2x + -7)(-4x + 18) = -24x + 100

Reorder the terms:
(-7 + 2x)(-4x + 18) = -24x + 100

Reorder the terms:
(-7 + 2x)(18 + -4x) = -24x + 100

Multiply (-7 + 2x) * (18 + -4x)
(-7(18 + -4x) + 2x * (18 + -4x)) = -24x + 100
((18 * -7 + -4x * -7) + 2x * (18 + -4x)) = -24x + 100
((-126 + 28x) + 2x * (18 + -4x)) = -24x + 100
(-126 + 28x + (18 * 2x + -4x * 2x)) = -24x + 100
(-126 + 28x + (36x + -8x2)) = -24x + 100

Combine like terms: 28x + 36x = 64x
(-126 + 64x + -8x2) = -24x + 100

Reorder the terms:
-126 + 64x + -8x2 = 100 + -24x

Solving
-126 + 64x + -8x2 = 100 + -24x

Solving for variable 'x'.

Reorder the terms:
-126 + -100 + 64x + 24x + -8x2 = 100 + -24x + -100 + 24x

Combine like terms: -126 + -100 = -226
-226 + 64x + 24x + -8x2 = 100 + -24x + -100 + 24x

Combine like terms: 64x + 24x = 88x
-226 + 88x + -8x2 = 100 + -24x + -100 + 24x

Reorder the terms:
-226 + 88x + -8x2 = 100 + -100 + -24x + 24x

Combine like terms: 100 + -100 = 0
-226 + 88x + -8x2 = 0 + -24x + 24x
-226 + 88x + -8x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-226 + 88x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-113 + 44x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-113 + 44x + -4x2)' equal to zero and attempt to solve:

Simplifying
-113 + 44x + -4x2 = 0

Solving
-113 + 44x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
28.25 + -11x + x2 = 0

Move the constant term to the right:

Add '-28.25' to each side of the equation.
28.25 + -11x + -28.25 + x2 = 0 + -28.25

Reorder the terms:
28.25 + -28.25 + -11x + x2 = 0 + -28.25

Combine like terms: 28.25 + -28.25 = 0.00
0.00 + -11x + x2 = 0 + -28.25
-11x + x2 = 0 + -28.25

Combine like terms: 0 + -28.25 = -28.25
-11x + x2 = -28.25

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -28.25 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -28.25 + 30.25

Combine like terms: -28.25 + 30.25 = 2
30.25 + -11x + x2 = 2

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -5.5) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -5.5 = 1.414213562

Simplifying
x + -5.5 = 1.414213562

Reorder the terms:
-5.5 + x = 1.414213562

Solving
-5.5 + x = 1.414213562

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 1.414213562 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 1.414213562 + 5.5
x = 1.414213562 + 5.5

Combine like terms: 1.414213562 + 5.5 = 6.914213562
x = 6.914213562

Simplifying
x = 6.914213562

Subproblem 2
x + -5.5 = -1.414213562

Simplifying
x + -5.5 = -1.414213562

Reorder the terms:
-5.5 + x = -1.414213562

Solving
-5.5 + x = -1.414213562

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -1.414213562 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -1.414213562 + 5.5
x = -1.414213562 + 5.5

Combine like terms: -1.414213562 + 5.5 = 4.085786438
x = 4.085786438

Simplifying
x = 4.085786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.914213562, 4.085786438}
Solution
x = {6.914213562, 4.085786438}