0=(x+5)(x-7)

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Solution for 0=(x+5)(x-7) equation: 


Simplifying
0 = (x + 5)(x + -7)

Reorder the terms:
0 = (5 + x)(x + -7)

Reorder the terms:
0 = (5 + x)(-7 + x)

Multiply (5 + x) * (-7 + x)
0 = (5(-7 + x) + x(-7 + x))
0 = ((-7 * 5 + x * 5) + x(-7 + x))
0 = ((-35 + 5x) + x(-7 + x))
0 = (-35 + 5x + (-7 * x + x * x))
0 = (-35 + 5x + (-7x + x2))

Combine like terms: 5x + -7x = -2x
0 = (-35 + -2x + x2)

Solving
0 = -35 + -2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 35 = 35
35 + 2x + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Reorder the terms:
35 + 2x + -1x2 = -35 + 35 + -2x + 2x + x2 + -1x2

Combine like terms: -35 + 35 = 0
35 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
35 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
35 + 2x + -1x2 = 0 + x2 + -1x2
35 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
35 + 2x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(5 + 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 '(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 = {7, -5}

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