(a+6)(a-15)=0

Solution for (a+6)(a-15)=0 equation:

Simplifying
(a + 6)(a + -15) = 0

Reorder the terms:
(6 + a)(a + -15) = 0

Reorder the terms:
(6 + a)(-15 + a) = 0

Multiply (6 + a) * (-15 + a)
(6(-15 + a) + a(-15 + a)) = 0
((-15 * 6 + a * 6) + a(-15 + a)) = 0
((-90 + 6a) + a(-15 + a)) = 0
(-90 + 6a + (-15 * a + a * a)) = 0
(-90 + 6a + (-15a + a2)) = 0

Combine like terms: 6a + -15a = -9a
(-90 + -9a + a2) = 0

Solving
-90 + -9a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(15 + -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 '(15 + -1a)' equal to zero and attempt to solve:

Simplifying
15 + -1a = 0

Solving
15 + -1a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1a = 0 + -15
-1a = 0 + -15

Combine like terms: 0 + -15 = -15
-1a = -15

Divide each side by '-1'.
a = 15

Simplifying
a = 15
Solution
a = {-6, 15}