2(2x+15)4x=180

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Solution for 2(2x+15)4x=180 equation: 


Simplifying
2(2x + 15) * 4x = 180

Reorder the terms:
2(15 + 2x) * 4x = 180

Reorder the terms for easier multiplication:
2 * 4x(15 + 2x) = 180

Multiply 2 * 4
8x(15 + 2x) = 180
(15 * 8x + 2x * 8x) = 180
(120x + 16x2) = 180

Solving
120x + 16x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 120x + 16x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 120x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 30x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 30x + 4x2)' equal to zero and attempt to solve:

Simplifying
-45 + 30x + 4x2 = 0

Solving
-45 + 30x + 4x2 = 0

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

Divide each side by '4'.
-11.25 + 7.5x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + 7.5x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + 7.5x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + 7.5x + x2 = 0 + 11.25
7.5x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
7.5x + x2 = 11.25

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 = 11.25 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 11.25 + 14.0625

Combine like terms: 11.25 + 14.0625 = 25.3125
14.0625 + 7.5x + x2 = 25.3125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 25.3125

Calculate the square root of the right side: 5.031152949

Break this problem into two subproblems by setting 
(x + 3.75) equal to 5.031152949 and -5.031152949.


Subproblem 1
x + 3.75 = 5.031152949

Simplifying
x + 3.75 = 5.031152949

Reorder the terms:
3.75 + x = 5.031152949

Solving
3.75 + x = 5.031152949

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 = 5.031152949 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 5.031152949 + -3.75
x = 5.031152949 + -3.75

Combine like terms: 5.031152949 + -3.75 = 1.281152949
x = 1.281152949

Simplifying
x = 1.281152949


Subproblem 2
x + 3.75 = -5.031152949

Simplifying
x + 3.75 = -5.031152949

Reorder the terms:
3.75 + x = -5.031152949

Solving
3.75 + x = -5.031152949

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 = -5.031152949 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -5.031152949 + -3.75
x = -5.031152949 + -3.75

Combine like terms: -5.031152949 + -3.75 = -8.781152949
x = -8.781152949

Simplifying
x = -8.781152949


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.281152949, -8.781152949}
Solution
x = {1.281152949, -8.781152949}

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