(x-8)(x+4)=13

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Solution for (x-8)(x+4)=13 equation: 


Simplifying
(x + -8)(x + 4) = 13

Reorder the terms:
(-8 + x)(x + 4) = 13

Reorder the terms:
(-8 + x)(4 + x) = 13

Multiply (-8 + x) * (4 + x)
(-8(4 + x) + x(4 + x)) = 13
((4 * -8 + x * -8) + x(4 + x)) = 13
((-32 + -8x) + x(4 + x)) = 13
(-32 + -8x + (4 * x + x * x)) = 13
(-32 + -8x + (4x + x2)) = 13

Combine like terms: -8x + 4x = -4x
(-32 + -4x + x2) = 13

Solving
-32 + -4x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-32 + -13 + -4x + x2 = 13 + -13

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

Combine like terms: 13 + -13 = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-5, 9}

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