-5(a-1)(9-a)=0

Solution for -5(a-1)(9-a)=0 equation:

Simplifying
-5(a + -1)(9 + -1a) = 0

Reorder the terms:
-5(-1 + a)(9 + -1a) = 0

Multiply (-1 + a) * (9 + -1a)
-5(-1(9 + -1a) + a(9 + -1a)) = 0
-5((9 * -1 + -1a * -1) + a(9 + -1a)) = 0
-5((-9 + 1a) + a(9 + -1a)) = 0
-5(-9 + 1a + (9 * a + -1a * a)) = 0
-5(-9 + 1a + (9a + -1a2)) = 0

Combine like terms: 1a + 9a = 10a
-5(-9 + 10a + -1a2) = 0
(-9 * -5 + 10a * -5 + -1a2 * -5) = 0
(45 + -50a + 5a2) = 0

Solving
45 + -50a + 5a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(9 + -10a + a2) = 0

Factor a trinomial.
5((1 + -1a)(9 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
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 = {1, 9}