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

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

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

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

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

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

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

Solving
-35 + -2a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-5, 7}