-6x-2=9x^2+6x+1

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Solution for -6x-2=9x^2+6x+1 equation: 


Simplifying
-6x + -2 = 9x2 + 6x + 1

Reorder the terms:
-2 + -6x = 9x2 + 6x + 1

Reorder the terms:
-2 + -6x = 1 + 6x + 9x2

Solving
-2 + -6x = 1 + 6x + 9x2

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + -6x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Combine like terms: -2 + -1 = -3
-3 + -6x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Combine like terms: -6x + -6x = -12x
-3 + -12x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Reorder the terms:
-3 + -12x + -9x2 = 1 + -1 + 6x + -6x + 9x2 + -9x2

Combine like terms: 1 + -1 = 0
-3 + -12x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2
-3 + -12x + -9x2 = 6x + -6x + 9x2 + -9x2

Combine like terms: 6x + -6x = 0
-3 + -12x + -9x2 = 0 + 9x2 + -9x2
-3 + -12x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-3 + -12x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + 4x + 3x2) = 0

Factor a trinomial.
-3((1 + x)(1 + 3x)) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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 + -1

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-1, -0.3333333333}

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