9x*9x+6x+3=6

Solution for 9x*9x+6x+3=6 equation:

Simplifying
9x * 9x + 6x + 3 = 6

Reorder the terms for easier multiplication:
9 * 9x * x + 6x + 3 = 6

Multiply 9 * 9
81x * x + 6x + 3 = 6

Multiply x * x
81x2 + 6x + 3 = 6

Reorder the terms:
3 + 6x + 81x2 = 6

Solving
3 + 6x + 81x2 = 6

Solving for variable 'x'.

Reorder the terms:
3 + -6 + 6x + 81x2 = 6 + -6

Combine like terms: 3 + -6 = -3
-3 + 6x + 81x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-3 + 6x + 81x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2x + 27x2) = 0

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

Simplifying
-1 + 2x + 27x2 = 0

Solving
-1 + 2x + 27x2 = 0

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

Divide each side by '27'.
-0.03703703704 + 0.07407407407x + x2 = 0

Move the constant term to the right:

Add '0.03703703704' to each side of the equation.
-0.03703703704 + 0.07407407407x + 0.03703703704 + x2 = 0 + 0.03703703704

Reorder the terms:
-0.03703703704 + 0.03703703704 + 0.07407407407x + x2 = 0 + 0.03703703704

Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000
0.00000000000 + 0.07407407407x + x2 = 0 + 0.03703703704
0.07407407407x + x2 = 0 + 0.03703703704

Combine like terms: 0 + 0.03703703704 = 0.03703703704
0.07407407407x + x2 = 0.03703703704

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 = 0.03703703704 + 0.001371742113

Reorder the terms:
0.001371742113 + 0.07407407407x + x2 = 0.03703703704 + 0.001371742113

Combine like terms: 0.03703703704 + 0.001371742113 = 0.038408779153
0.001371742113 + 0.07407407407x + x2 = 0.038408779153

Factor a perfect square on the left side:
(x + 0.03703703704)(x + 0.03703703704) = 0.038408779153

Calculate the square root of the right side: 0.195981579

Break this problem into two subproblems by setting 
(x + 0.03703703704) equal to 0.195981579 and -0.195981579.

Subproblem 1
x + 0.03703703704 = 0.195981579

Simplifying
x + 0.03703703704 = 0.195981579

Reorder the terms:
0.03703703704 + x = 0.195981579

Solving
0.03703703704 + x = 0.195981579

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 = 0.195981579 + -0.03703703704

Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000
0.00000000000 + x = 0.195981579 + -0.03703703704
x = 0.195981579 + -0.03703703704

Combine like terms: 0.195981579 + -0.03703703704 = 0.15894454196
x = 0.15894454196

Simplifying
x = 0.15894454196

Subproblem 2
x + 0.03703703704 = -0.195981579

Simplifying
x + 0.03703703704 = -0.195981579

Reorder the terms:
0.03703703704 + x = -0.195981579

Solving
0.03703703704 + x = -0.195981579

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 = -0.195981579 + -0.03703703704

Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000
0.00000000000 + x = -0.195981579 + -0.03703703704
x = -0.195981579 + -0.03703703704

Combine like terms: -0.195981579 + -0.03703703704 = -0.23301861604
x = -0.23301861604

Simplifying
x = -0.23301861604

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15894454196, -0.23301861604}
Solution
x = {0.15894454196, -0.23301861604}