9x^2+17x-6=9-5x

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Solution for 9x^2+17x-6=9-5x equation: 


Simplifying
9x2 + 17x + -6 = 9 + -5x

Reorder the terms:
-6 + 17x + 9x2 = 9 + -5x

Solving
-6 + 17x + 9x2 = 9 + -5x

Solving for variable 'x'.

Reorder the terms:
-6 + -9 + 17x + 5x + 9x2 = 9 + -5x + -9 + 5x

Combine like terms: -6 + -9 = -15
-15 + 17x + 5x + 9x2 = 9 + -5x + -9 + 5x

Combine like terms: 17x + 5x = 22x
-15 + 22x + 9x2 = 9 + -5x + -9 + 5x

Reorder the terms:
-15 + 22x + 9x2 = 9 + -9 + -5x + 5x

Combine like terms: 9 + -9 = 0
-15 + 22x + 9x2 = 0 + -5x + 5x
-15 + 22x + 9x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-15 + 22x + 9x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -9x) = 0


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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

Solving
5 + -9x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x = 0 + -5
-9x = 0 + -5

Combine like terms: 0 + -5 = -5
-9x = -5

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {-3, 0.5555555556}

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