(x+9)(x-5)=-13

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Solution for (x+9)(x-5)=-13 equation: 


Simplifying
(x + 9)(x + -5) = -13

Reorder the terms:
(9 + x)(x + -5) = -13

Reorder the terms:
(9 + x)(-5 + x) = -13

Multiply (9 + x) * (-5 + x)
(9(-5 + x) + x(-5 + x)) = -13
((-5 * 9 + x * 9) + x(-5 + x)) = -13
((-45 + 9x) + x(-5 + x)) = -13
(-45 + 9x + (-5 * x + x * x)) = -13
(-45 + 9x + (-5x + x2)) = -13

Combine like terms: 9x + -5x = 4x
(-45 + 4x + x2) = -13

Solving
-45 + 4x + x2 = -13

Solving for variable 'x'.

Reorder the terms:
-45 + 13 + 4x + x2 = -13 + 13

Combine like terms: -45 + 13 = -32
-32 + 4x + x2 = -13 + 13

Combine like terms: -13 + 13 = 0
-32 + 4x + x2 = 0

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