9=3x^2-2x-7

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Solution for 9=3x^2-2x-7 equation: 


Simplifying
9 = 3x2 + -2x + -7

Reorder the terms:
9 = -7 + -2x + 3x2

Solving
9 = -7 + -2x + 3x2

Solving for variable 'x'.

Combine like terms: 9 + 7 = 16
16 + 2x + -3x2 = -7 + -2x + 3x2 + 7 + 2x + -3x2

Reorder the terms:
16 + 2x + -3x2 = -7 + 7 + -2x + 2x + 3x2 + -3x2

Combine like terms: -7 + 7 = 0
16 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
16 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
16 + 2x + -3x2 = 0 + 3x2 + -3x2
16 + 2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
16 + 2x + -3x2 = 0

Factor a trinomial.
(8 + -3x)(2 + x) = 0


Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {2.666666667, -2}

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