(3x+11)90(4x-5)=180

Solution for (3x+11)90(4x-5)=180 equation:

Simplifying
(3x + 11) * 90(4x + -5) = 180

Reorder the terms:
(11 + 3x) * 90(4x + -5) = 180

Reorder the terms:
(11 + 3x) * 90(-5 + 4x) = 180

Reorder the terms for easier multiplication:
90(11 + 3x)(-5 + 4x) = 180

Multiply (11 + 3x) * (-5 + 4x)
90(11(-5 + 4x) + 3x * (-5 + 4x)) = 180
90((-5 * 11 + 4x * 11) + 3x * (-5 + 4x)) = 180
90((-55 + 44x) + 3x * (-5 + 4x)) = 180
90(-55 + 44x + (-5 * 3x + 4x * 3x)) = 180
90(-55 + 44x + (-15x + 12x2)) = 180

Combine like terms: 44x + -15x = 29x
90(-55 + 29x + 12x2) = 180
(-55 * 90 + 29x * 90 + 12x2 * 90) = 180
(-4950 + 2610x + 1080x2) = 180

Solving
-4950 + 2610x + 1080x2 = 180

Solving for variable 'x'.

Reorder the terms:
-4950 + -180 + 2610x + 1080x2 = 180 + -180

Combine like terms: -4950 + -180 = -5130
-5130 + 2610x + 1080x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-5130 + 2610x + 1080x2 = 0

Factor out the Greatest Common Factor (GCF), '90'.
90(-57 + 29x + 12x2) = 0

Ignore the factor 90.
Subproblem 1
Set the factor '(-57 + 29x + 12x2)' equal to zero and attempt to solve:

Simplifying
-57 + 29x + 12x2 = 0

Solving
-57 + 29x + 12x2 = 0

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

Divide each side by '12'.
-4.75 + 2.416666667x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 2.416666667x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 2.416666667x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 2.416666667x + x2 = 0 + 4.75
2.416666667x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
2.416666667x + x2 = 4.75

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 = 4.75 + 1.460069446

Reorder the terms:
1.460069446 + 2.416666667x + x2 = 4.75 + 1.460069446

Combine like terms: 4.75 + 1.460069446 = 6.210069446
1.460069446 + 2.416666667x + x2 = 6.210069446

Factor a perfect square on the left side:
(x + 1.208333334)(x + 1.208333334) = 6.210069446

Calculate the square root of the right side: 2.492001093

Break this problem into two subproblems by setting 
(x + 1.208333334) equal to 2.492001093 and -2.492001093.

Subproblem 1
x + 1.208333334 = 2.492001093

Simplifying
x + 1.208333334 = 2.492001093

Reorder the terms:
1.208333334 + x = 2.492001093

Solving
1.208333334 + x = 2.492001093

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 = 2.492001093 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = 2.492001093 + -1.208333334
x = 2.492001093 + -1.208333334

Combine like terms: 2.492001093 + -1.208333334 = 1.283667759
x = 1.283667759

Simplifying
x = 1.283667759

Subproblem 2
x + 1.208333334 = -2.492001093

Simplifying
x + 1.208333334 = -2.492001093

Reorder the terms:
1.208333334 + x = -2.492001093

Solving
1.208333334 + x = -2.492001093

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 = -2.492001093 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + x = -2.492001093 + -1.208333334
x = -2.492001093 + -1.208333334

Combine like terms: -2.492001093 + -1.208333334 = -3.700334427
x = -3.700334427

Simplifying
x = -3.700334427

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.283667759, -3.700334427}
Solution
x = {1.283667759, -3.700334427}