(a-4)(a+9)=0

Solution for (a-4)(a+9)=0 equation:

Simplifying
(a + -4)(a + 9) = 0

Reorder the terms:
(-4 + a)(a + 9) = 0

Reorder the terms:
(-4 + a)(9 + a) = 0

Multiply (-4 + a) * (9 + a)
(-4(9 + a) + a(9 + a)) = 0
((9 * -4 + a * -4) + a(9 + a)) = 0
((-36 + -4a) + a(9 + a)) = 0
(-36 + -4a + (9 * a + a * a)) = 0
(-36 + -4a + (9a + a2)) = 0

Combine like terms: -4a + 9a = 5a
(-36 + 5a + a2) = 0

Solving
-36 + 5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
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 = {-9, 4}