9x-9x^2+2x+3x^2-6x-3x=0+2-6

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Solution for 9x-9x^2+2x+3x^2-6x-3x=0+2-6 equation: 


Simplifying
9x + -9x2 + 2x + 3x2 + -6x + -3x = 0 + 2 + -6

Reorder the terms:
9x + 2x + -6x + -3x + -9x2 + 3x2 = 0 + 2 + -6

Combine like terms: 9x + 2x = 11x
11x + -6x + -3x + -9x2 + 3x2 = 0 + 2 + -6

Combine like terms: 11x + -6x = 5x
5x + -3x + -9x2 + 3x2 = 0 + 2 + -6

Combine like terms: 5x + -3x = 2x
2x + -9x2 + 3x2 = 0 + 2 + -6

Combine like terms: -9x2 + 3x2 = -6x2
2x + -6x2 = 0 + 2 + -6

Combine like terms: 0 + 2 = 2
2x + -6x2 = 2 + -6

Combine like terms: 2 + -6 = -4
2x + -6x2 = -4

Solving
2x + -6x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 2x + -6x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 2x + -6x2 = 0

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

Factor a trinomial.
2((1 + -1x)(2 + 3x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1, -0.6666666667}

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