180=(4x+30)2x

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Solution for 180=(4x+30)2x equation: 


Simplifying
180 = (4x + 30) * 2x

Reorder the terms:
180 = (30 + 4x) * 2x

Reorder the terms for easier multiplication:
180 = 2x(30 + 4x)
180 = (30 * 2x + 4x * 2x)
180 = (60x + 8x2)

Solving
180 = 60x + 8x2

Solving for variable 'x'.

Reorder the terms:
180 + -60x + -8x2 = 60x + -60x + 8x2 + -8x2

Combine like terms: 60x + -60x = 0
180 + -60x + -8x2 = 0 + 8x2 + -8x2
180 + -60x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
180 + -60x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -15x + -2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(45 + -15x + -2x2)' equal to zero and attempt to solve:

Simplifying
45 + -15x + -2x2 = 0

Solving
45 + -15x + -2x2 = 0

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

Divide each side by '-2'.
-22.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 7.5x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 7.5x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 7.5x + x2 = 0 + 22.5
7.5x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
7.5x + x2 = 22.5

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 = 22.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 22.5 + 14.0625

Combine like terms: 22.5 + 14.0625 = 36.5625
14.0625 + 7.5x + x2 = 36.5625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 36.5625

Calculate the square root of the right side: 6.046693311

Break this problem into two subproblems by setting 
(x + 3.75) equal to 6.046693311 and -6.046693311.


Subproblem 1
x + 3.75 = 6.046693311

Simplifying
x + 3.75 = 6.046693311

Reorder the terms:
3.75 + x = 6.046693311

Solving
3.75 + x = 6.046693311

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 = 6.046693311 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 6.046693311 + -3.75
x = 6.046693311 + -3.75

Combine like terms: 6.046693311 + -3.75 = 2.296693311
x = 2.296693311

Simplifying
x = 2.296693311


Subproblem 2
x + 3.75 = -6.046693311

Simplifying
x + 3.75 = -6.046693311

Reorder the terms:
3.75 + x = -6.046693311

Solving
3.75 + x = -6.046693311

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 = -6.046693311 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -6.046693311 + -3.75
x = -6.046693311 + -3.75

Combine like terms: -6.046693311 + -3.75 = -9.796693311
x = -9.796693311

Simplifying
x = -9.796693311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.296693311, -9.796693311}
Solution
x = {2.296693311, -9.796693311}

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