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

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

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

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

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

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

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

Solving
-30 + -1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(6 + -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 '(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
Solution
a = {-5, 6}