-x^2+17x-23=5x+9

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Solution for -x^2+17x-23=5x+9 equation: 


Simplifying
-1x2 + 17x + -23 = 5x + 9

Reorder the terms:
-23 + 17x + -1x2 = 5x + 9

Reorder the terms:
-23 + 17x + -1x2 = 9 + 5x

Solving
-23 + 17x + -1x2 = 9 + 5x

Solving for variable 'x'.

Reorder the terms:
-23 + -9 + 17x + -5x + -1x2 = 9 + 5x + -9 + -5x

Combine like terms: -23 + -9 = -32
-32 + 17x + -5x + -1x2 = 9 + 5x + -9 + -5x

Combine like terms: 17x + -5x = 12x
-32 + 12x + -1x2 = 9 + 5x + -9 + -5x

Reorder the terms:
-32 + 12x + -1x2 = 9 + -9 + 5x + -5x

Combine like terms: 9 + -9 = 0
-32 + 12x + -1x2 = 0 + 5x + -5x
-32 + 12x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-32 + 12x + -1x2 = 0

Factor a trinomial.
(-8 + x)(4 + -1x) = 0


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

Simplifying
-8 + x = 0

Solving
-8 + x = 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 + x = 0 + 8

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

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

Simplifying
x = 8

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {8, 4}

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