12x-17=15-9x^2

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Solution for 12x-17=15-9x^2 equation: 


Simplifying
12x + -17 = 15 + -9x2

Reorder the terms:
-17 + 12x = 15 + -9x2

Solving
-17 + 12x = 15 + -9x2

Solving for variable 'x'.

Reorder the terms:
-17 + -15 + 12x + 9x2 = 15 + -9x2 + -15 + 9x2

Combine like terms: -17 + -15 = -32
-32 + 12x + 9x2 = 15 + -9x2 + -15 + 9x2

Reorder the terms:
-32 + 12x + 9x2 = 15 + -15 + -9x2 + 9x2

Combine like terms: 15 + -15 = 0
-32 + 12x + 9x2 = 0 + -9x2 + 9x2
-32 + 12x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-32 + 12x + 9x2 = 0

Factor a trinomial.
(-8 + -3x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-2.666666667, 1.333333333}

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