(9x*9x)+6x-6=0

Solution for (9x*9x)+6x-6=0 equation:

Simplifying
(9x * 9x) + 6x + -6 = 0

Reorder the terms for easier multiplication:
(9 * 9x * x) + 6x + -6 = 0

Multiply 9 * 9
(81x * x) + 6x + -6 = 0

Multiply x * x
(81x2) + 6x + -6 = 0

Reorder the terms:
-6 + 6x + (81x2) = 0

Solving
-6 + 6x + (81x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 2x + (27x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 2x + (27x2))' equal to zero and attempt to solve:

Simplifying
-2 + 2x + (27x2) = 0

Solving
-2 + 2x + (27x2) = 0

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

Divide each side by '27'.
-0.07407407407 + 0.07407407407x + x2 = 0

Move the constant term to the right:

Add '0.07407407407' to each side of the equation.
-0.07407407407 + 0.07407407407x + 0.07407407407 + x2 = 0 + 0.07407407407

Reorder the terms:
-0.07407407407 + 0.07407407407 + 0.07407407407x + x2 = 0 + 0.07407407407

Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000
0.00000000000 + 0.07407407407x + x2 = 0 + 0.07407407407
0.07407407407x + x2 = 0 + 0.07407407407

Combine like terms: 0 + 0.07407407407 = 0.07407407407
0.07407407407x + x2 = 0.07407407407

The x term is 0.07407407407x.  Take half its coefficient (0.03703703704).
Square it (0.001371742113) and add it to both sides.

Add '0.001371742113' to each side of the equation.
0.07407407407x + 0.001371742113 + x2 = 0.07407407407 + 0.001371742113

Reorder the terms:
0.001371742113 + 0.07407407407x + x2 = 0.07407407407 + 0.001371742113

Combine like terms: 0.07407407407 + 0.001371742113 = 0.075445816183
0.001371742113 + 0.07407407407x + x2 = 0.075445816183

Factor a perfect square on the left side:
((x) + 0.03703703704)((x) + 0.03703703704) = 0.075445816183

Calculate the square root of the right side: 0.274674018

Break this problem into two subproblems by setting 
((x) + 0.03703703704) equal to 0.274674018 and -0.274674018.

Subproblem 1
(x) + 0.03703703704 = 0.274674018

Simplifying
(x) + 0.03703703704 = 0.274674018
x + 0.03703703704 = 0.274674018

Reorder the terms:
0.03703703704 + x = 0.274674018

Solving
0.03703703704 + x = 0.274674018

Solving for variable 'x'.

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

Add '-0.03703703704' to each side of the equation.
0.03703703704 + -0.03703703704 + x = 0.274674018 + -0.03703703704

Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000
0.00000000000 + x = 0.274674018 + -0.03703703704
x = 0.274674018 + -0.03703703704

Combine like terms: 0.274674018 + -0.03703703704 = 0.23763698096
x = 0.23763698096

Simplifying
x = 0.23763698096

Subproblem 2
(x) + 0.03703703704 = -0.274674018

Simplifying
(x) + 0.03703703704 = -0.274674018
x + 0.03703703704 = -0.274674018

Reorder the terms:
0.03703703704 + x = -0.274674018

Solving
0.03703703704 + x = -0.274674018

Solving for variable 'x'.

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

Add '-0.03703703704' to each side of the equation.
0.03703703704 + -0.03703703704 + x = -0.274674018 + -0.03703703704

Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000
0.00000000000 + x = -0.274674018 + -0.03703703704
x = -0.274674018 + -0.03703703704

Combine like terms: -0.274674018 + -0.03703703704 = -0.31171105504
x = -0.31171105504

Simplifying
x = -0.31171105504

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.23763698096, -0.31171105504}
Solution
x = {0.23763698096, -0.31171105504}