5x+7=x^2-x-9

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Solution for 5x+7=x^2-x-9 equation: 


Simplifying
5x + 7 = x2 + -1x + -9

Reorder the terms:
7 + 5x = x2 + -1x + -9

Reorder the terms:
7 + 5x = -9 + -1x + x2

Solving
7 + 5x = -9 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
7 + 9 + 5x + x + -1x2 = -9 + -1x + x2 + 9 + x + -1x2

Combine like terms: 7 + 9 = 16
16 + 5x + x + -1x2 = -9 + -1x + x2 + 9 + x + -1x2

Combine like terms: 5x + x = 6x
16 + 6x + -1x2 = -9 + -1x + x2 + 9 + x + -1x2

Reorder the terms:
16 + 6x + -1x2 = -9 + 9 + -1x + x + x2 + -1x2

Combine like terms: -9 + 9 = 0
16 + 6x + -1x2 = 0 + -1x + x + x2 + -1x2
16 + 6x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
16 + 6x + -1x2 = 0 + x2 + -1x2
16 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + 6x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(2 + x) = 0


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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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 = {8, -2}

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