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

Solution for (5-a)(a+15)=0 equation:

Simplifying
(5 + -1a)(a + 15) = 0

Reorder the terms:
(5 + -1a)(15 + a) = 0

Multiply (5 + -1a) * (15 + a)
(5(15 + a) + -1a * (15 + a)) = 0
((15 * 5 + a * 5) + -1a * (15 + a)) = 0
((75 + 5a) + -1a * (15 + a)) = 0
(75 + 5a + (15 * -1a + a * -1a)) = 0
(75 + 5a + (-15a + -1a2)) = 0

Combine like terms: 5a + -15a = -10a
(75 + -10a + -1a2) = 0

Solving
75 + -10a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -1a)(15 + a) = 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 '(15 + a)' equal to zero and attempt to solve:

Simplifying
15 + a = 0

Solving
15 + a = 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 + a = 0 + -15

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

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

Simplifying
a = -15
Solution
a = {5, -15}