4x(x+90)=180

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Solution for 4x(x+90)=180 equation: 


Simplifying
4x(x + 90) = 180

Reorder the terms:
4x(90 + x) = 180
(90 * 4x + x * 4x) = 180
(360x + 4x2) = 180

Solving
360x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 360x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 360x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 90x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 90x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 90x + x2 = 0

Solving
-45 + 90x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 90x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 90x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 90x + x2 = 0 + 45
90x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
90x + x2 = 45

The x term is 90x.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90x + 2025 + x2 = 45 + 2025

Reorder the terms:
2025 + 90x + x2 = 45 + 2025

Combine like terms: 45 + 2025 = 2070
2025 + 90x + x2 = 2070

Factor a perfect square on the left side:
(x + 45)(x + 45) = 2070

Calculate the square root of the right side: 45.497252664

Break this problem into two subproblems by setting 
(x + 45) equal to 45.497252664 and -45.497252664.


Subproblem 1
x + 45 = 45.497252664

Simplifying
x + 45 = 45.497252664

Reorder the terms:
45 + x = 45.497252664

Solving
45 + x = 45.497252664

Solving for variable 'x'.

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

Add '-45' to each side of the equation.
45 + -45 + x = 45.497252664 + -45

Combine like terms: 45 + -45 = 0
0 + x = 45.497252664 + -45
x = 45.497252664 + -45

Combine like terms: 45.497252664 + -45 = 0.497252664
x = 0.497252664

Simplifying
x = 0.497252664


Subproblem 2
x + 45 = -45.497252664

Simplifying
x + 45 = -45.497252664

Reorder the terms:
45 + x = -45.497252664

Solving
45 + x = -45.497252664

Solving for variable 'x'.

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

Add '-45' to each side of the equation.
45 + -45 + x = -45.497252664 + -45

Combine like terms: 45 + -45 = 0
0 + x = -45.497252664 + -45
x = -45.497252664 + -45

Combine like terms: -45.497252664 + -45 = -90.497252664
x = -90.497252664

Simplifying
x = -90.497252664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.497252664, -90.497252664}
Solution
x = {0.497252664, -90.497252664}

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