(-5x+45)(11x+21)=90

Solution for (-5x+45)(11x+21)=90 equation:

Simplifying
(-5x + 45)(11x + 21) = 90

Reorder the terms:
(45 + -5x)(11x + 21) = 90

Reorder the terms:
(45 + -5x)(21 + 11x) = 90

Multiply (45 + -5x) * (21 + 11x)
(45(21 + 11x) + -5x * (21 + 11x)) = 90
((21 * 45 + 11x * 45) + -5x * (21 + 11x)) = 90
((945 + 495x) + -5x * (21 + 11x)) = 90
(945 + 495x + (21 * -5x + 11x * -5x)) = 90
(945 + 495x + (-105x + -55x2)) = 90

Combine like terms: 495x + -105x = 390x
(945 + 390x + -55x2) = 90

Solving
945 + 390x + -55x2 = 90

Solving for variable 'x'.

Reorder the terms:
945 + -90 + 390x + -55x2 = 90 + -90

Combine like terms: 945 + -90 = 855
855 + 390x + -55x2 = 90 + -90

Combine like terms: 90 + -90 = 0
855 + 390x + -55x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(171 + 78x + -11x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(171 + 78x + -11x2)' equal to zero and attempt to solve:

Simplifying
171 + 78x + -11x2 = 0

Solving
171 + 78x + -11x2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-15.54545455 + -7.090909091x + x2 = 0

Move the constant term to the right:

Add '15.54545455' to each side of the equation.
-15.54545455 + -7.090909091x + 15.54545455 + x2 = 0 + 15.54545455

Reorder the terms:
-15.54545455 + 15.54545455 + -7.090909091x + x2 = 0 + 15.54545455

Combine like terms: -15.54545455 + 15.54545455 = 0.00000000
0.00000000 + -7.090909091x + x2 = 0 + 15.54545455
-7.090909091x + x2 = 0 + 15.54545455

Combine like terms: 0 + 15.54545455 = 15.54545455
-7.090909091x + x2 = 15.54545455

The x term is -7.090909091x.  Take half its coefficient (-3.545454546).
Square it (12.57024794) and add it to both sides.

Add '12.57024794' to each side of the equation.
-7.090909091x + 12.57024794 + x2 = 15.54545455 + 12.57024794

Reorder the terms:
12.57024794 + -7.090909091x + x2 = 15.54545455 + 12.57024794

Combine like terms: 15.54545455 + 12.57024794 = 28.11570249
12.57024794 + -7.090909091x + x2 = 28.11570249

Factor a perfect square on the left side:
(x + -3.545454546)(x + -3.545454546) = 28.11570249

Calculate the square root of the right side: 5.302424209

Break this problem into two subproblems by setting 
(x + -3.545454546) equal to 5.302424209 and -5.302424209.

Subproblem 1
x + -3.545454546 = 5.302424209

Simplifying
x + -3.545454546 = 5.302424209

Reorder the terms:
-3.545454546 + x = 5.302424209

Solving
-3.545454546 + x = 5.302424209

Solving for variable 'x'.

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

Add '3.545454546' to each side of the equation.
-3.545454546 + 3.545454546 + x = 5.302424209 + 3.545454546

Combine like terms: -3.545454546 + 3.545454546 = 0.000000000
0.000000000 + x = 5.302424209 + 3.545454546
x = 5.302424209 + 3.545454546

Combine like terms: 5.302424209 + 3.545454546 = 8.847878755
x = 8.847878755

Simplifying
x = 8.847878755

Subproblem 2
x + -3.545454546 = -5.302424209

Simplifying
x + -3.545454546 = -5.302424209

Reorder the terms:
-3.545454546 + x = -5.302424209

Solving
-3.545454546 + x = -5.302424209

Solving for variable 'x'.

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

Add '3.545454546' to each side of the equation.
-3.545454546 + 3.545454546 + x = -5.302424209 + 3.545454546

Combine like terms: -3.545454546 + 3.545454546 = 0.000000000
0.000000000 + x = -5.302424209 + 3.545454546
x = -5.302424209 + 3.545454546

Combine like terms: -5.302424209 + 3.545454546 = -1.756969663
x = -1.756969663

Simplifying
x = -1.756969663

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.847878755, -1.756969663}
Solution
x = {8.847878755, -1.756969663}