(4x-5)(3x+11)=90

Solution for (4x-5)(3x+11)=90 equation:

Simplifying
(4x + -5)(3x + 11) = 90

Reorder the terms:
(-5 + 4x)(3x + 11) = 90

Reorder the terms:
(-5 + 4x)(11 + 3x) = 90

Multiply (-5 + 4x) * (11 + 3x)
(-5(11 + 3x) + 4x * (11 + 3x)) = 90
((11 * -5 + 3x * -5) + 4x * (11 + 3x)) = 90
((-55 + -15x) + 4x * (11 + 3x)) = 90
(-55 + -15x + (11 * 4x + 3x * 4x)) = 90
(-55 + -15x + (44x + 12x2)) = 90

Combine like terms: -15x + 44x = 29x
(-55 + 29x + 12x2) = 90

Solving
-55 + 29x + 12x2 = 90

Solving for variable 'x'.

Reorder the terms:
-55 + -90 + 29x + 12x2 = 90 + -90

Combine like terms: -55 + -90 = -145
-145 + 29x + 12x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-145 + 29x + 12x2 = 0

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

Divide each side by '12'.
-12.08333333 + 2.416666667x + x2 = 0

Move the constant term to the right:

Add '12.08333333' to each side of the equation.
-12.08333333 + 2.416666667x + 12.08333333 + x2 = 0 + 12.08333333

Reorder the terms:
-12.08333333 + 12.08333333 + 2.416666667x + x2 = 0 + 12.08333333

Combine like terms: -12.08333333 + 12.08333333 = 0.00000000
0.00000000 + 2.416666667x + x2 = 0 + 12.08333333
2.416666667x + x2 = 0 + 12.08333333

Combine like terms: 0 + 12.08333333 = 12.08333333
2.416666667x + x2 = 12.08333333

The x term is 2.416666667x.  Take half its coefficient (1.208333334).
Square it (1.460069446) and add it to both sides.

Add '1.460069446' to each side of the equation.
2.416666667x + 1.460069446 + x2 = 12.08333333 + 1.460069446

Reorder the terms:
1.460069446 + 2.416666667x + x2 = 12.08333333 + 1.460069446

Combine like terms: 12.08333333 + 1.460069446 = 13.543402776
1.460069446 + 2.416666667x + x2 = 13.543402776

Factor a perfect square on the left side:
(x + 1.208333334)(x + 1.208333334) = 13.543402776

Calculate the square root of the right side: 3.680136244

Break this problem into two subproblems by setting 
(x + 1.208333334) equal to 3.680136244 and -3.680136244.

Subproblem 1
x + 1.208333334 = 3.680136244

Simplifying
x + 1.208333334 = 3.680136244

Reorder the terms:
1.208333334 + x = 3.680136244

Solving
1.208333334 + x = 3.680136244

Solving for variable 'x'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + x = 3.680136244 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = 3.680136244 + -1.208333334
x = 3.680136244 + -1.208333334

Combine like terms: 3.680136244 + -1.208333334 = 2.47180291
x = 2.47180291

Simplifying
x = 2.47180291

Subproblem 2
x + 1.208333334 = -3.680136244

Simplifying
x + 1.208333334 = -3.680136244

Reorder the terms:
1.208333334 + x = -3.680136244

Solving
1.208333334 + x = -3.680136244

Solving for variable 'x'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + x = -3.680136244 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = -3.680136244 + -1.208333334
x = -3.680136244 + -1.208333334

Combine like terms: -3.680136244 + -1.208333334 = -4.888469578
x = -4.888469578

Simplifying
x = -4.888469578

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.47180291, -4.888469578}