4x(2x+16)=180

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Solution for 4x(2x+16)=180 equation:


Simplifying
4x(2x + 16) = 180

Reorder the terms:
4x(16 + 2x) = 180
(16 * 4x + 2x * 4x) = 180
(64x + 8x2) = 180

Solving
64x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 64x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 64x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 16x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 16x + 2x2)' equal to zero and attempt to solve:

Simplifying
-45 + 16x + 2x2 = 0

Solving
-45 + 16x + 2x2 = 0

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

Divide each side by '2'.
-22.5 + 8x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 8x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 8x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 8x + x2 = 0 + 22.5
8x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
8x + x2 = 22.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 22.5 + 16

Reorder the terms:
16 + 8x + x2 = 22.5 + 16

Combine like terms: 22.5 + 16 = 38.5
16 + 8x + x2 = 38.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 38.5

Calculate the square root of the right side: 6.204836823

Break this problem into two subproblems by setting 
(x + 4) equal to 6.204836823 and -6.204836823.


Subproblem 1
x + 4 = 6.204836823

Simplifying
x + 4 = 6.204836823

Reorder the terms:
4 + x = 6.204836823

Solving
4 + x = 6.204836823

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.204836823 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.204836823 + -4
x = 6.204836823 + -4

Combine like terms: 6.204836823 + -4 = 2.204836823
x = 2.204836823

Simplifying
x = 2.204836823


Subproblem 2
x + 4 = -6.204836823

Simplifying
x + 4 = -6.204836823

Reorder the terms:
4 + x = -6.204836823

Solving
4 + x = -6.204836823

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.204836823 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.204836823 + -4
x = -6.204836823 + -4

Combine like terms: -6.204836823 + -4 = -10.204836823
x = -10.204836823

Simplifying
x = -10.204836823


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.204836823, -10.204836823}
Solution
x = {2.204836823, -10.204836823}

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