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

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


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

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

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

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

Combine like terms: 7x + -5x = 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.
(5 + -1x)(7 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {5, -7}

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