180=3x(x+12)

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Solution for 180=3x(x+12) equation: 


Simplifying
180 = 3x(x + 12)

Reorder the terms:
180 = 3x(12 + x)
180 = (12 * 3x + x * 3x)
180 = (36x + 3x2)

Solving
180 = 36x + 3x2

Solving for variable 'x'.

Reorder the terms:
180 + -36x + -3x2 = 36x + -36x + 3x2 + -3x2

Combine like terms: 36x + -36x = 0
180 + -36x + -3x2 = 0 + 3x2 + -3x2
180 + -36x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
180 + -36x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(60 + -12x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(60 + -12x + -1x2)' equal to zero and attempt to solve:

Simplifying
60 + -12x + -1x2 = 0

Solving
60 + -12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-60 + 12x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 12x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 12x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 12x + x2 = 0 + 60
12x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
12x + x2 = 60

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 60 + 36

Reorder the terms:
36 + 12x + x2 = 60 + 36

Combine like terms: 60 + 36 = 96
36 + 12x + x2 = 96

Factor a perfect square on the left side:
(x + 6)(x + 6) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + 6) equal to 9.797958971 and -9.797958971.


Subproblem 1
x + 6 = 9.797958971

Simplifying
x + 6 = 9.797958971

Reorder the terms:
6 + x = 9.797958971

Solving
6 + x = 9.797958971

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 9.797958971 + -6

Combine like terms: 6 + -6 = 0
0 + x = 9.797958971 + -6
x = 9.797958971 + -6

Combine like terms: 9.797958971 + -6 = 3.797958971
x = 3.797958971

Simplifying
x = 3.797958971


Subproblem 2
x + 6 = -9.797958971

Simplifying
x + 6 = -9.797958971

Reorder the terms:
6 + x = -9.797958971

Solving
6 + x = -9.797958971

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -9.797958971 + -6

Combine like terms: 6 + -6 = 0
0 + x = -9.797958971 + -6
x = -9.797958971 + -6

Combine like terms: -9.797958971 + -6 = -15.797958971
x = -15.797958971

Simplifying
x = -15.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.797958971, -15.797958971}
Solution
x = {3.797958971, -15.797958971}

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