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

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

Simplifying
(5 + -1a)(2a + 5) = 0

Reorder the terms:
(5 + -1a)(5 + 2a) = 0

Multiply (5 + -1a) * (5 + 2a)
(5(5 + 2a) + -1a * (5 + 2a)) = 0
((5 * 5 + 2a * 5) + -1a * (5 + 2a)) = 0
((25 + 10a) + -1a * (5 + 2a)) = 0
(25 + 10a + (5 * -1a + 2a * -1a)) = 0
(25 + 10a + (-5a + -2a2)) = 0

Combine like terms: 10a + -5a = 5a
(25 + 5a + -2a2) = 0

Solving
25 + 5a + -2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -1a)(5 + 2a) = 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 '(5 + 2a)' equal to zero and attempt to solve:

Simplifying
5 + 2a = 0

Solving
5 + 2a = 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 + 2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2a = 0 + -5
2a = 0 + -5

Combine like terms: 0 + -5 = -5
2a = -5

Divide each side by '2'.
a = -2.5

Simplifying
a = -2.5
Solution
a = {5, -2.5}