-x^2-4x+93=5x+23

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Solution for -x^2-4x+93=5x+23 equation: 


Simplifying
-1x2 + -4x + 93 = 5x + 23

Reorder the terms:
93 + -4x + -1x2 = 5x + 23

Reorder the terms:
93 + -4x + -1x2 = 23 + 5x

Solving
93 + -4x + -1x2 = 23 + 5x

Solving for variable 'x'.

Reorder the terms:
93 + -23 + -4x + -5x + -1x2 = 23 + 5x + -23 + -5x

Combine like terms: 93 + -23 = 70
70 + -4x + -5x + -1x2 = 23 + 5x + -23 + -5x

Combine like terms: -4x + -5x = -9x
70 + -9x + -1x2 = 23 + 5x + -23 + -5x

Reorder the terms:
70 + -9x + -1x2 = 23 + -23 + 5x + -5x

Combine like terms: 23 + -23 = 0
70 + -9x + -1x2 = 0 + 5x + -5x
70 + -9x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
70 + -9x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(14 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {5, -14}

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