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

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

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

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

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

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

Combine like terms: 3x + -5x = -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.
(-4 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-4, 6}