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

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

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

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

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

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

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

Solving
-35 + -2x + x2 = 0

Solving for variable 'x'.

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