x(2x+15)=180

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Solution for x(2x+15)=180 equation: 


Simplifying
x(2x + 15) = 180

Reorder the terms:
x(15 + 2x) = 180
(15 * x + 2x * x) = 180
(15x + 2x2) = 180

Solving
15x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 15x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 15x + 2x2 = 0

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

Divide each side by '2'.
-90 + 7.5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 7.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 7.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 7.5x + x2 = 0 + 90
7.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
7.5x + x2 = 90

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 90 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 90 + 14.0625

Combine like terms: 90 + 14.0625 = 104.0625
14.0625 + 7.5x + x2 = 104.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 104.0625

Calculate the square root of the right side: 10.201102882

Break this problem into two subproblems by setting 
(x + 3.75) equal to 10.201102882 and -10.201102882.


Subproblem 1
x + 3.75 = 10.201102882

Simplifying
x + 3.75 = 10.201102882

Reorder the terms:
3.75 + x = 10.201102882

Solving
3.75 + x = 10.201102882

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 10.201102882 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 10.201102882 + -3.75
x = 10.201102882 + -3.75

Combine like terms: 10.201102882 + -3.75 = 6.451102882
x = 6.451102882

Simplifying
x = 6.451102882


Subproblem 2
x + 3.75 = -10.201102882

Simplifying
x + 3.75 = -10.201102882

Reorder the terms:
3.75 + x = -10.201102882

Solving
3.75 + x = -10.201102882

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -10.201102882 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -10.201102882 + -3.75
x = -10.201102882 + -3.75

Combine like terms: -10.201102882 + -3.75 = -13.951102882
x = -13.951102882

Simplifying
x = -13.951102882


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.451102882, -13.951102882}

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