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

Solution for (2a-5)(a+1)=0 equation:

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

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

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

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

Combine like terms: -5a + 2a = -3a
(-5 + -3a + 2a2) = 0

Solving
-5 + -3a + 2a2 = 0

Solving for variable 'a'.

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

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 '(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 = {-1, 2.5}