(x-3)(x+5)-9=0

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Solution for (x-3)(x+5)-9=0 equation: 


Simplifying
(x + -3)(x + 5) + -9 = 0

Reorder the terms:
(-3 + x)(x + 5) + -9 = 0

Reorder the terms:
(-3 + x)(5 + x) + -9 = 0

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) + -9 = 0
((5 * -3 + x * -3) + x(5 + x)) + -9 = 0
((-15 + -3x) + x(5 + x)) + -9 = 0
(-15 + -3x + (5 * x + x * x)) + -9 = 0
(-15 + -3x + (5x + x2)) + -9 = 0

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) + -9 = 0

Reorder the terms:
-15 + -9 + 2x + x2 = 0

Combine like terms: -15 + -9 = -24
-24 + 2x + x2 = 0

Solving
-24 + 2x + x2 = 0

Solving for variable 'x'.

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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