3(x+3)2(3+x)=180

Solution for 3(x+3)2(3+x)=180 equation:

Simplifying
3(x + 3) * 2(3 + x) = 180

Reorder the terms:
3(3 + x) * 2(3 + x) = 180

Reorder the terms for easier multiplication:
3 * 2(3 + x)(3 + x) = 180

Multiply 3 * 2
6(3 + x)(3 + x) = 180

Multiply (3 + x) * (3 + x)
6(3(3 + x) + x(3 + x)) = 180
6((3 * 3 + x * 3) + x(3 + x)) = 180
6((9 + 3x) + x(3 + x)) = 180
6(9 + 3x + (3 * x + x * x)) = 180
6(9 + 3x + (3x + x2)) = 180

Combine like terms: 3x + 3x = 6x
6(9 + 6x + x2) = 180
(9 * 6 + 6x * 6 + x2 * 6) = 180
(54 + 36x + 6x2) = 180

Solving
54 + 36x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
54 + -180 + 36x + 6x2 = 180 + -180

Combine like terms: 54 + -180 = -126
-126 + 36x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-126 + 36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 6x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-21 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + 6x + x2 = 0

Solving
-21 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 6x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 6x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 6x + x2 = 0 + 21
6x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
6x + x2 = 21

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 21 + 9

Reorder the terms:
9 + 6x + x2 = 21 + 9

Combine like terms: 21 + 9 = 30
9 + 6x + x2 = 30

Factor a perfect square on the left side:
(x + 3)(x + 3) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 3) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + 3 = 5.477225575

Simplifying
x + 3 = 5.477225575

Reorder the terms:
3 + x = 5.477225575

Solving
3 + x = 5.477225575

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 5.477225575 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.477225575 + -3
x = 5.477225575 + -3

Combine like terms: 5.477225575 + -3 = 2.477225575
x = 2.477225575

Simplifying
x = 2.477225575

Subproblem 2
x + 3 = -5.477225575

Simplifying
x + 3 = -5.477225575

Reorder the terms:
3 + x = -5.477225575

Solving
3 + x = -5.477225575

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -5.477225575 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.477225575 + -3
x = -5.477225575 + -3

Combine like terms: -5.477225575 + -3 = -8.477225575
x = -8.477225575

Simplifying
x = -8.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.477225575, -8.477225575}
Solution
x = {2.477225575, -8.477225575}