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

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

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

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

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

Multiply (-5 + a) * (7 + a)
(-5(7 + a) + a(7 + a)) = 0
((7 * -5 + a * -5) + a(7 + a)) = 0
((-35 + -5a) + a(7 + a)) = 0
(-35 + -5a + (7 * a + a * a)) = 0
(-35 + -5a + (7a + a2)) = 0

Combine like terms: -5a + 7a = 2a
(-35 + 2a + a2) = 0

Solving
-35 + 2a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -1a)(5 + -1a) = 0

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

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

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

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

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

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

Simplifying
a = -7
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

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

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

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

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