x=5x^2+9x+6

Solution for x=5x^2+9x+6 equation:

Simplifying
x = 5x2 + 9x + 6

Reorder the terms:
x = 6 + 9x + 5x2

Solving
x = 6 + 9x + 5x2

Solving for variable 'x'.

Reorder the terms:
-6 + x + -9x + -5x2 = 6 + 9x + 5x2 + -6 + -9x + -5x2

Combine like terms: x + -9x = -8x
-6 + -8x + -5x2 = 6 + 9x + 5x2 + -6 + -9x + -5x2

Reorder the terms:
-6 + -8x + -5x2 = 6 + -6 + 9x + -9x + 5x2 + -5x2

Combine like terms: 6 + -6 = 0
-6 + -8x + -5x2 = 0 + 9x + -9x + 5x2 + -5x2
-6 + -8x + -5x2 = 9x + -9x + 5x2 + -5x2

Combine like terms: 9x + -9x = 0
-6 + -8x + -5x2 = 0 + 5x2 + -5x2
-6 + -8x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + -8x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 8x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 8x + 5x2)' equal to zero and attempt to solve:

Simplifying
6 + 8x + 5x2 = 0

Solving
6 + 8x + 5x2 = 0

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

Divide each side by '5'.
1.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 1.6x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 1.6x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 1.6x + x2 = 0 + -1.2
1.6x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
1.6x + x2 = -1.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = -1.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = -1.2 + 0.64

Combine like terms: -1.2 + 0.64 = -0.56
0.64 + 1.6x + x2 = -0.56

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = -0.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.