(a-5)(a+6)=0

Solution for (a-5)(a+6)=0 equation:

Simplifying
(a + -5)(a + 6) = 0

Reorder the terms:
(-5 + a)(a + 6) = 0

Reorder the terms:
(-5 + a)(6 + a) = 0

Multiply (-5 + a) * (6 + a)
(-5(6 + a) + a(6 + a)) = 0
((6 * -5 + a * -5) + a(6 + a)) = 0
((-30 + -5a) + a(6 + a)) = 0
(-30 + -5a + (6 * a + a * a)) = 0
(-30 + -5a + (6a + a2)) = 0

Combine like terms: -5a + 6a = 1a
(-30 + 1a + a2) = 0

Solving
-30 + 1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
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 = {-6, 5}