(a-4)(a-5)=

Solution for (a-4)(a-5)= 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 = -9a
(20 + -9a + a2) = 0

Solving
20 + -9a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -1a)(5 + -1a) = 0

Subproblem 1
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
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 = {4, 5}