(x+5)(x-3)=9

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Solution for (x+5)(x-3)=9 equation: 


Simplifying
(x + 5)(x + -3) = 9

Reorder the terms:
(5 + x)(x + -3) = 9

Reorder the terms:
(5 + x)(-3 + x) = 9

Multiply (5 + x) * (-3 + x)
(5(-3 + x) + x(-3 + x)) = 9
((-3 * 5 + x * 5) + x(-3 + x)) = 9
((-15 + 5x) + x(-3 + x)) = 9
(-15 + 5x + (-3 * x + x * x)) = 9
(-15 + 5x + (-3x + x2)) = 9

Combine like terms: 5x + -3x = 2x
(-15 + 2x + x2) = 9

Solving
-15 + 2x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-15 + -9 + 2x + x2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 2x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 4}

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