(2a+5)(3-a)=0

Solution for (2a+5)(3-a)=0 equation:

Simplifying
(2a + 5)(3 + -1a) = 0

Reorder the terms:
(5 + 2a)(3 + -1a) = 0

Multiply (5 + 2a) * (3 + -1a)
(5(3 + -1a) + 2a * (3 + -1a)) = 0
((3 * 5 + -1a * 5) + 2a * (3 + -1a)) = 0
((15 + -5a) + 2a * (3 + -1a)) = 0
(15 + -5a + (3 * 2a + -1a * 2a)) = 0
(15 + -5a + (6a + -2a2)) = 0

Combine like terms: -5a + 6a = 1a
(15 + 1a + -2a2) = 0

Solving
15 + 1a + -2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -1a)(5 + 2a) = 0

Subproblem 1
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
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 = {3, -2.5}