9x(x-4)=9x-33

Solution for 9x(x-4)=9x-33 equation:

Simplifying
9x(x + -4) = 9x + -33

Reorder the terms:
9x(-4 + x) = 9x + -33
(-4 * 9x + x * 9x) = 9x + -33
(-36x + 9x2) = 9x + -33

Reorder the terms:
-36x + 9x2 = -33 + 9x

Solving
-36x + 9x2 = -33 + 9x

Solving for variable 'x'.

Reorder the terms:
33 + -36x + -9x + 9x2 = -33 + 9x + 33 + -9x

Combine like terms: -36x + -9x = -45x
33 + -45x + 9x2 = -33 + 9x + 33 + -9x

Reorder the terms:
33 + -45x + 9x2 = -33 + 33 + 9x + -9x

Combine like terms: -33 + 33 = 0
33 + -45x + 9x2 = 0 + 9x + -9x
33 + -45x + 9x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
33 + -45x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -15x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(11 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
11 + -15x + 3x2 = 0

Solving
11 + -15x + 3x2 = 0

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

Divide each side by '3'.
3.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -5x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -5x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + -3.666666667
-5x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-5x + x2 = -3.666666667

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 = -3.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.666666667 + 6.25

Combine like terms: -3.666666667 + 6.25 = 2.583333333
6.25 + -5x + x2 = 2.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.583333333

Calculate the square root of the right side: 1.607275127

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.607275127 and -1.607275127.

Subproblem 1
x + -2.5 = 1.607275127

Simplifying
x + -2.5 = 1.607275127

Reorder the terms:
-2.5 + x = 1.607275127

Solving
-2.5 + x = 1.607275127

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 = 1.607275127 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.607275127 + 2.5
x = 1.607275127 + 2.5

Combine like terms: 1.607275127 + 2.5 = 4.107275127
x = 4.107275127

Simplifying
x = 4.107275127

Subproblem 2
x + -2.5 = -1.607275127

Simplifying
x + -2.5 = -1.607275127

Reorder the terms:
-2.5 + x = -1.607275127

Solving
-2.5 + x = -1.607275127

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 = -1.607275127 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.607275127 + 2.5
x = -1.607275127 + 2.5

Combine like terms: -1.607275127 + 2.5 = 0.892724873
x = 0.892724873

Simplifying
x = 0.892724873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.107275127, 0.892724873}
Solution
x = {4.107275127, 0.892724873}