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

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

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

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

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

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

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

Solving
-35 + 2x + x2 = 0

Solving for variable 'x'.

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