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

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


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

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

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

Multiply (5 + x) * (-9 + x)
0 = (5(-9 + x) + x(-9 + x))
0 = ((-9 * 5 + x * 5) + x(-9 + x))
0 = ((-45 + 5x) + x(-9 + x))
0 = (-45 + 5x + (-9 * x + x * x))
0 = (-45 + 5x + (-9x + x2))

Combine like terms: 5x + -9x = -4x
0 = (-45 + -4x + x2)

Solving
0 = -45 + -4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 45 = 45
45 + 4x + -1x2 = -45 + -4x + x2 + 45 + 4x + -1x2

Reorder the terms:
45 + 4x + -1x2 = -45 + 45 + -4x + 4x + x2 + -1x2

Combine like terms: -45 + 45 = 0
45 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2
45 + 4x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
45 + 4x + -1x2 = 0 + x2 + -1x2
45 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + 4x + -1x2 = 0

Factor a trinomial.
(9 + -1x)(5 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

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

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