9x(3x+18)=30

Solution for 9x(3x+18)=30 equation:

Simplifying
9x(3x + 18) = 30

Reorder the terms:
9x(18 + 3x) = 30
(18 * 9x + 3x * 9x) = 30
(162x + 27x2) = 30

Solving
162x + 27x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 162x + 27x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 162x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 54x + 9x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + 54x + 9x2)' equal to zero and attempt to solve:

Simplifying
-10 + 54x + 9x2 = 0

Solving
-10 + 54x + 9x2 = 0

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

Divide each side by '9'.
-1.111111111 + 6x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 6x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 6x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 6x + x2 = 0 + 1.111111111
6x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
6x + x2 = 1.111111111

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 = 1.111111111 + 9

Reorder the terms:
9 + 6x + x2 = 1.111111111 + 9

Combine like terms: 1.111111111 + 9 = 10.111111111
9 + 6x + x2 = 10.111111111

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10.111111111

Calculate the square root of the right side: 3.179797338

Break this problem into two subproblems by setting 
(x + 3) equal to 3.179797338 and -3.179797338.

Subproblem 1
x + 3 = 3.179797338

Simplifying
x + 3 = 3.179797338

Reorder the terms:
3 + x = 3.179797338

Solving
3 + x = 3.179797338

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 = 3.179797338 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.179797338 + -3
x = 3.179797338 + -3

Combine like terms: 3.179797338 + -3 = 0.179797338
x = 0.179797338

Simplifying
x = 0.179797338

Subproblem 2
x + 3 = -3.179797338

Simplifying
x + 3 = -3.179797338

Reorder the terms:
3 + x = -3.179797338

Solving
3 + x = -3.179797338

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 = -3.179797338 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.179797338 + -3
x = -3.179797338 + -3

Combine like terms: -3.179797338 + -3 = -6.179797338
x = -6.179797338

Simplifying
x = -6.179797338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.179797338, -6.179797338}
Solution
x = {0.179797338, -6.179797338}