9x^2-18x=-6

Solution for 9x^2-18x=-6 equation:

Simplifying
9x2 + -18x = -6

Reorder the terms:
-18x + 9x2 = -6

Solving
-18x + 9x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + -18x + 9x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -6x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + -6x + 3x2 = 0

Solving
2 + -6x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.6666666667
-2x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2x + x2 = -0.6666666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.6666666667 + 1

Reorder the terms:
1 + -2x + x2 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + -2x + x2 = 0.3333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(x + -1) equal to 0.577350269 and -0.577350269.

Subproblem 1
x + -1 = 0.577350269

Simplifying
x + -1 = 0.577350269

Reorder the terms:
-1 + x = 0.577350269

Solving
-1 + x = 0.577350269

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.577350269 + 1
x = 0.577350269 + 1

Combine like terms: 0.577350269 + 1 = 1.577350269
x = 1.577350269

Simplifying
x = 1.577350269

Subproblem 2
x + -1 = -0.577350269

Simplifying
x + -1 = -0.577350269

Reorder the terms:
-1 + x = -0.577350269

Solving
-1 + x = -0.577350269

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.577350269 + 1
x = -0.577350269 + 1

Combine like terms: -0.577350269 + 1 = 0.422649731
x = 0.422649731

Simplifying
x = 0.422649731

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.577350269, 0.422649731}
Solution
x = {1.577350269, 0.422649731}