(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.
(-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}