(a-4)(a+5)=0

Solution for (a-4)(a+5)=0 equation:

Simplifying
(a + -4)(a + 5) = 0

Reorder the terms:
(-4 + a)(a + 5) = 0

Reorder the terms:
(-4 + a)(5 + a) = 0

Multiply (-4 + a) * (5 + a)
(-4(5 + a) + a(5 + a)) = 0
((5 * -4 + a * -4) + a(5 + a)) = 0
((-20 + -4a) + a(5 + a)) = 0
(-20 + -4a + (5 * a + a * a)) = 0
(-20 + -4a + (5a + a2)) = 0

Combine like terms: -4a + 5a = 1a
(-20 + 1a + a2) = 0

Solving
-20 + 1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-5, 4}