(7x-14)(4x+18)=90

Solution for (7x-14)(4x+18)=90 equation:

Simplifying
(7x + -14)(4x + 18) = 90

Reorder the terms:
(-14 + 7x)(4x + 18) = 90

Reorder the terms:
(-14 + 7x)(18 + 4x) = 90

Multiply (-14 + 7x) * (18 + 4x)
(-14(18 + 4x) + 7x * (18 + 4x)) = 90
((18 * -14 + 4x * -14) + 7x * (18 + 4x)) = 90
((-252 + -56x) + 7x * (18 + 4x)) = 90
(-252 + -56x + (18 * 7x + 4x * 7x)) = 90
(-252 + -56x + (126x + 28x2)) = 90

Combine like terms: -56x + 126x = 70x
(-252 + 70x + 28x2) = 90

Solving
-252 + 70x + 28x2 = 90

Solving for variable 'x'.

Reorder the terms:
-252 + -90 + 70x + 28x2 = 90 + -90

Combine like terms: -252 + -90 = -342
-342 + 70x + 28x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-342 + 70x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-171 + 35x + 14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-171 + 35x + 14x2)' equal to zero and attempt to solve:

Simplifying
-171 + 35x + 14x2 = 0

Solving
-171 + 35x + 14x2 = 0

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

Divide each side by '14'.
-12.21428571 + 2.5x + x2 = 0

Move the constant term to the right:

Add '12.21428571' to each side of the equation.
-12.21428571 + 2.5x + 12.21428571 + x2 = 0 + 12.21428571

Reorder the terms:
-12.21428571 + 12.21428571 + 2.5x + x2 = 0 + 12.21428571

Combine like terms: -12.21428571 + 12.21428571 = 0.00000000
0.00000000 + 2.5x + x2 = 0 + 12.21428571
2.5x + x2 = 0 + 12.21428571

Combine like terms: 0 + 12.21428571 = 12.21428571
2.5x + x2 = 12.21428571

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 12.21428571 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 12.21428571 + 1.5625

Combine like terms: 12.21428571 + 1.5625 = 13.77678571
1.5625 + 2.5x + x2 = 13.77678571

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 13.77678571

Calculate the square root of the right side: 3.711709271

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.711709271 and -3.711709271.

Subproblem 1
x + 1.25 = 3.711709271

Simplifying
x + 1.25 = 3.711709271

Reorder the terms:
1.25 + x = 3.711709271

Solving
1.25 + x = 3.711709271

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.711709271 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.711709271 + -1.25
x = 3.711709271 + -1.25

Combine like terms: 3.711709271 + -1.25 = 2.461709271
x = 2.461709271

Simplifying
x = 2.461709271

Subproblem 2
x + 1.25 = -3.711709271

Simplifying
x + 1.25 = -3.711709271

Reorder the terms:
1.25 + x = -3.711709271

Solving
1.25 + x = -3.711709271

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.711709271 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.711709271 + -1.25
x = -3.711709271 + -1.25

Combine like terms: -3.711709271 + -1.25 = -4.961709271
x = -4.961709271

Simplifying
x = -4.961709271

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.461709271, -4.961709271}
Solution
x = {2.461709271, -4.961709271}