-4x(x+6)+165=5x-9(x-9)

Solution for -4x(x+6)+165=5x-9(x-9) equation:

Simplifying
-4x(x + 6) + 165 = 5x + -9(x + -9)

Reorder the terms:
-4x(6 + x) + 165 = 5x + -9(x + -9)
(6 * -4x + x * -4x) + 165 = 5x + -9(x + -9)
(-24x + -4x2) + 165 = 5x + -9(x + -9)

Reorder the terms:
165 + -24x + -4x2 = 5x + -9(x + -9)

Reorder the terms:
165 + -24x + -4x2 = 5x + -9(-9 + x)
165 + -24x + -4x2 = 5x + (-9 * -9 + x * -9)
165 + -24x + -4x2 = 5x + (81 + -9x)

Reorder the terms:
165 + -24x + -4x2 = 81 + 5x + -9x

Combine like terms: 5x + -9x = -4x
165 + -24x + -4x2 = 81 + -4x

Solving
165 + -24x + -4x2 = 81 + -4x

Solving for variable 'x'.

Reorder the terms:
165 + -81 + -24x + 4x + -4x2 = 81 + -4x + -81 + 4x

Combine like terms: 165 + -81 = 84
84 + -24x + 4x + -4x2 = 81 + -4x + -81 + 4x

Combine like terms: -24x + 4x = -20x
84 + -20x + -4x2 = 81 + -4x + -81 + 4x

Reorder the terms:
84 + -20x + -4x2 = 81 + -81 + -4x + 4x

Combine like terms: 81 + -81 = 0
84 + -20x + -4x2 = 0 + -4x + 4x
84 + -20x + -4x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
84 + -20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + -5x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(21 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
21 + -5x + -1x2 = 0

Solving
21 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + 5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 5x + x2 = 0 + 21
5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
5x + x2 = 21

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 21 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 21 + 6.25

Combine like terms: 21 + 6.25 = 27.25
6.25 + 5x + x2 = 27.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + 2.5 = 5.220153254

Simplifying
x + 2.5 = 5.220153254

Reorder the terms:
2.5 + x = 5.220153254

Solving
2.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 5.220153254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.220153254 + -2.5
x = 5.220153254 + -2.5

Combine like terms: 5.220153254 + -2.5 = 2.720153254
x = 2.720153254

Simplifying
x = 2.720153254

Subproblem 2
x + 2.5 = -5.220153254

Simplifying
x + 2.5 = -5.220153254

Reorder the terms:
2.5 + x = -5.220153254

Solving
2.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -5.220153254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.220153254 + -2.5
x = -5.220153254 + -2.5

Combine like terms: -5.220153254 + -2.5 = -7.720153254
x = -7.720153254

Simplifying
x = -7.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.720153254, -7.720153254}
Solution
x = {2.720153254, -7.720153254}