(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.
(-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}