(9x+54)(9x+54)-15=3

Solution for (9x+54)(9x+54)-15=3 equation:

Simplifying
(9x + 54)(9x + 54) + -15 = 3

Reorder the terms:
(54 + 9x)(9x + 54) + -15 = 3

Reorder the terms:
(54 + 9x)(54 + 9x) + -15 = 3

Multiply (54 + 9x) * (54 + 9x)
(54(54 + 9x) + 9x * (54 + 9x)) + -15 = 3
((54 * 54 + 9x * 54) + 9x * (54 + 9x)) + -15 = 3
((2916 + 486x) + 9x * (54 + 9x)) + -15 = 3
(2916 + 486x + (54 * 9x + 9x * 9x)) + -15 = 3
(2916 + 486x + (486x + 81x2)) + -15 = 3

Combine like terms: 486x + 486x = 972x
(2916 + 972x + 81x2) + -15 = 3

Reorder the terms:
2916 + -15 + 972x + 81x2 = 3

Combine like terms: 2916 + -15 = 2901
2901 + 972x + 81x2 = 3

Solving
2901 + 972x + 81x2 = 3

Solving for variable 'x'.

Reorder the terms:
2901 + -3 + 972x + 81x2 = 3 + -3

Combine like terms: 2901 + -3 = 2898
2898 + 972x + 81x2 = 3 + -3

Combine like terms: 3 + -3 = 0
2898 + 972x + 81x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(322 + 108x + 9x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(322 + 108x + 9x2)' equal to zero and attempt to solve:

Simplifying
322 + 108x + 9x2 = 0

Solving
322 + 108x + 9x2 = 0

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

Divide each side by '9'.
35.77777778 + 12x + x2 = 0

Move the constant term to the right:

Add '-35.77777778' to each side of the equation.
35.77777778 + 12x + -35.77777778 + x2 = 0 + -35.77777778

Reorder the terms:
35.77777778 + -35.77777778 + 12x + x2 = 0 + -35.77777778

Combine like terms: 35.77777778 + -35.77777778 = 0.00000000
0.00000000 + 12x + x2 = 0 + -35.77777778
12x + x2 = 0 + -35.77777778

Combine like terms: 0 + -35.77777778 = -35.77777778
12x + x2 = -35.77777778

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 = -35.77777778 + 36

Reorder the terms:
36 + 12x + x2 = -35.77777778 + 36

Combine like terms: -35.77777778 + 36 = 0.22222222
36 + 12x + x2 = 0.22222222

Factor a perfect square on the left side:
(x + 6)(x + 6) = 0.22222222

Calculate the square root of the right side: 0.471404518

Break this problem into two subproblems by setting 
(x + 6) equal to 0.471404518 and -0.471404518.

Subproblem 1
x + 6 = 0.471404518

Simplifying
x + 6 = 0.471404518

Reorder the terms:
6 + x = 0.471404518

Solving
6 + x = 0.471404518

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 = 0.471404518 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0.471404518 + -6
x = 0.471404518 + -6

Combine like terms: 0.471404518 + -6 = -5.528595482
x = -5.528595482

Simplifying
x = -5.528595482

Subproblem 2
x + 6 = -0.471404518

Simplifying
x + 6 = -0.471404518

Reorder the terms:
6 + x = -0.471404518

Solving
6 + x = -0.471404518

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 = -0.471404518 + -6

Combine like terms: 6 + -6 = 0
0 + x = -0.471404518 + -6
x = -0.471404518 + -6

Combine like terms: -0.471404518 + -6 = -6.471404518
x = -6.471404518

Simplifying
x = -6.471404518

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.528595482, -6.471404518}
Solution
x = {-5.528595482, -6.471404518}