0=(x-7)(x+13)

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Solution for 0=(x-7)(x+13) equation: 


Simplifying
0 = (x + -7)(x + 13)

Reorder the terms:
0 = (-7 + x)(x + 13)

Reorder the terms:
0 = (-7 + x)(13 + x)

Multiply (-7 + x) * (13 + x)
0 = (-7(13 + x) + x(13 + x))
0 = ((13 * -7 + x * -7) + x(13 + x))
0 = ((-91 + -7x) + x(13 + x))
0 = (-91 + -7x + (13 * x + x * x))
0 = (-91 + -7x + (13x + x2))

Combine like terms: -7x + 13x = 6x
0 = (-91 + 6x + x2)

Solving
0 = -91 + 6x + x2

Solving for variable 'x'.

Combine like terms: 0 + 91 = 91
91 + -6x + -1x2 = -91 + 6x + x2 + 91 + -6x + -1x2

Reorder the terms:
91 + -6x + -1x2 = -91 + 91 + 6x + -6x + x2 + -1x2

Combine like terms: -91 + 91 = 0
91 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
91 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
91 + -6x + -1x2 = 0 + x2 + -1x2
91 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
91 + -6x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(13 + x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {7, -13}

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