(a-5)(a-2)=0

Solution for (a-5)(a-2)=0 equation:

Simplifying
(a + -5)(a + -2) = 0

Reorder the terms:
(-5 + a)(a + -2) = 0

Reorder the terms:
(-5 + a)(-2 + a) = 0

Multiply (-5 + a) * (-2 + a)
(-5(-2 + a) + a(-2 + a)) = 0
((-2 * -5 + a * -5) + a(-2 + a)) = 0
((10 + -5a) + a(-2 + a)) = 0
(10 + -5a + (-2 * a + a * a)) = 0
(10 + -5a + (-2a + a2)) = 0

Combine like terms: -5a + -2a = -7a
(10 + -7a + a2) = 0

Solving
10 + -7a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, 5}