4x(x+30)=180

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


Simplifying
4x(x + 30) = 180

Reorder the terms:
4x(30 + x) = 180
(30 * 4x + x * 4x) = 180
(120x + 4x2) = 180

Solving
120x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 120x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 120x + 4x2 = 0

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

Ignore the factor 4.

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

Simplifying
-45 + 30x + x2 = 0

Solving
-45 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 30x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 30x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 30x + x2 = 0 + 45
30x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
30x + x2 = 45

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 45 + 225

Reorder the terms:
225 + 30x + x2 = 45 + 225

Combine like terms: 45 + 225 = 270
225 + 30x + x2 = 270

Factor a perfect square on the left side:
(x + 15)(x + 15) = 270

Calculate the square root of the right side: 16.431676725

Break this problem into two subproblems by setting 
(x + 15) equal to 16.431676725 and -16.431676725.


Subproblem 1
x + 15 = 16.431676725

Simplifying
x + 15 = 16.431676725

Reorder the terms:
15 + x = 16.431676725

Solving
15 + x = 16.431676725

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 16.431676725 + -15

Combine like terms: 15 + -15 = 0
0 + x = 16.431676725 + -15
x = 16.431676725 + -15

Combine like terms: 16.431676725 + -15 = 1.431676725
x = 1.431676725

Simplifying
x = 1.431676725


Subproblem 2
x + 15 = -16.431676725

Simplifying
x + 15 = -16.431676725

Reorder the terms:
15 + x = -16.431676725

Solving
15 + x = -16.431676725

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -16.431676725 + -15

Combine like terms: 15 + -15 = 0
0 + x = -16.431676725 + -15
x = -16.431676725 + -15

Combine like terms: -16.431676725 + -15 = -31.431676725
x = -31.431676725

Simplifying
x = -31.431676725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.431676725, -31.431676725}
Solution
x = {1.431676725, -31.431676725}

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