(a-9)*(a-5)=

Solution for (a-9)*(a-5)= equation:

Simplifying
(a + -9)(a + -5) = 0

Reorder the terms:
(-9 + a)(a + -5) = 0

Reorder the terms:
(-9 + a)(-5 + a) = 0

Multiply (-9 + a) * (-5 + a)
(-9(-5 + a) + a(-5 + a)) = 0
((-5 * -9 + a * -9) + a(-5 + a)) = 0
((45 + -9a) + a(-5 + a)) = 0
(45 + -9a + (-5 * a + a * a)) = 0
(45 + -9a + (-5a + a2)) = 0

Combine like terms: -9a + -5a = -14a
(45 + -14a + a2) = 0

Solving
45 + -14a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -1a)(9 + -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 '(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
Solution
a = {5, 9}