(2x-1)+(3x-32)+(2x+13)3x=360

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Solution for (2x-1)+(3x-32)+(2x+13)3x=360 equation: 


Simplifying
(2x + -1) + (3x + -32) + (2x + 13) * 3x = 360

Reorder the terms:
(-1 + 2x) + (3x + -32) + (2x + 13) * 3x = 360

Remove parenthesis around (-1 + 2x)
-1 + 2x + (3x + -32) + (2x + 13) * 3x = 360

Reorder the terms:
-1 + 2x + (-32 + 3x) + (2x + 13) * 3x = 360

Remove parenthesis around (-32 + 3x)
-1 + 2x + -32 + 3x + (2x + 13) * 3x = 360

Reorder the terms:
-1 + 2x + -32 + 3x + (13 + 2x) * 3x = 360

Reorder the terms for easier multiplication:
-1 + 2x + -32 + 3x + 3x(13 + 2x) = 360
-1 + 2x + -32 + 3x + (13 * 3x + 2x * 3x) = 360
-1 + 2x + -32 + 3x + (39x + 6x2) = 360

Reorder the terms:
-1 + -32 + 2x + 3x + 39x + 6x2 = 360

Combine like terms: -1 + -32 = -33
-33 + 2x + 3x + 39x + 6x2 = 360

Combine like terms: 2x + 3x = 5x
-33 + 5x + 39x + 6x2 = 360

Combine like terms: 5x + 39x = 44x
-33 + 44x + 6x2 = 360

Solving
-33 + 44x + 6x2 = 360

Solving for variable 'x'.

Reorder the terms:
-33 + -360 + 44x + 6x2 = 360 + -360

Combine like terms: -33 + -360 = -393
-393 + 44x + 6x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-393 + 44x + 6x2 = 0

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

Divide each side by '6'.
-65.5 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '65.5' to each side of the equation.
-65.5 + 7.333333333x + 65.5 + x2 = 0 + 65.5

Reorder the terms:
-65.5 + 65.5 + 7.333333333x + x2 = 0 + 65.5

Combine like terms: -65.5 + 65.5 = 0.0
0.0 + 7.333333333x + x2 = 0 + 65.5
7.333333333x + x2 = 0 + 65.5

Combine like terms: 0 + 65.5 = 65.5
7.333333333x + x2 = 65.5

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 65.5 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 65.5 + 13.44444445

Combine like terms: 65.5 + 13.44444445 = 78.94444445
13.44444445 + 7.333333333x + x2 = 78.94444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 78.94444445

Calculate the square root of the right side: 8.885068624

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 8.885068624 and -8.885068624.


Subproblem 1
x + 3.666666667 = 8.885068624

Simplifying
x + 3.666666667 = 8.885068624

Reorder the terms:
3.666666667 + x = 8.885068624

Solving
3.666666667 + x = 8.885068624

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 8.885068624 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 8.885068624 + -3.666666667
x = 8.885068624 + -3.666666667

Combine like terms: 8.885068624 + -3.666666667 = 5.218401957
x = 5.218401957

Simplifying
x = 5.218401957


Subproblem 2
x + 3.666666667 = -8.885068624

Simplifying
x + 3.666666667 = -8.885068624

Reorder the terms:
3.666666667 + x = -8.885068624

Solving
3.666666667 + x = -8.885068624

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -8.885068624 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -8.885068624 + -3.666666667
x = -8.885068624 + -3.666666667

Combine like terms: -8.885068624 + -3.666666667 = -12.551735291
x = -12.551735291

Simplifying
x = -12.551735291


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.218401957, -12.551735291}

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