(9x)+4x+5x(-2x+15)=33

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Solution for (9x)+4x+5x(-2x+15)=33 equation: 


Simplifying
(9x) + 4x + 5x(-2x + 15) = 33

Reorder the terms:
(9x) + 4x + 5x(15 + -2x) = 33
(9x) + 4x + (15 * 5x + -2x * 5x) = 33
(9x) + 4x + (75x + -10x2) = 33

Combine like terms: (9x) + 4x = 13x
13x + 75x + -10x2 = 33

Combine like terms: 13x + 75x = 88x
88x + -10x2 = 33

Solving
88x + -10x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 88x + -10x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 88x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
3.3 + -8.8x + x2 = 0.0

Move the constant term to the right:

Add '-3.3' to each side of the equation.
3.3 + -8.8x + -3.3 + x2 = 0.0 + -3.3

Reorder the terms:
3.3 + -3.3 + -8.8x + x2 = 0.0 + -3.3

Combine like terms: 3.3 + -3.3 = 0.0
0.0 + -8.8x + x2 = 0.0 + -3.3
-8.8x + x2 = 0.0 + -3.3

Combine like terms: 0.0 + -3.3 = -3.3
-8.8x + x2 = -3.3

The x term is -8.8x.  Take half its coefficient (-4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
-8.8x + 19.36 + x2 = -3.3 + 19.36

Reorder the terms:
19.36 + -8.8x + x2 = -3.3 + 19.36

Combine like terms: -3.3 + 19.36 = 16.06
19.36 + -8.8x + x2 = 16.06

Factor a perfect square on the left side:
(x + -4.4)(x + -4.4) = 16.06

Calculate the square root of the right side: 4.007492982

Break this problem into two subproblems by setting 
(x + -4.4) equal to 4.007492982 and -4.007492982.


Subproblem 1
x + -4.4 = 4.007492982

Simplifying
x + -4.4 = 4.007492982

Reorder the terms:
-4.4 + x = 4.007492982

Solving
-4.4 + x = 4.007492982

Solving for variable 'x'.

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

Add '4.4' to each side of the equation.
-4.4 + 4.4 + x = 4.007492982 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = 4.007492982 + 4.4
x = 4.007492982 + 4.4

Combine like terms: 4.007492982 + 4.4 = 8.407492982
x = 8.407492982

Simplifying
x = 8.407492982


Subproblem 2
x + -4.4 = -4.007492982

Simplifying
x + -4.4 = -4.007492982

Reorder the terms:
-4.4 + x = -4.007492982

Solving
-4.4 + x = -4.007492982

Solving for variable 'x'.

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

Add '4.4' to each side of the equation.
-4.4 + 4.4 + x = -4.007492982 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = -4.007492982 + 4.4
x = -4.007492982 + 4.4

Combine like terms: -4.007492982 + 4.4 = 0.392507018
x = 0.392507018

Simplifying
x = 0.392507018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.407492982, 0.392507018}

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