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

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

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

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

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

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

Combine like terms: -10a + 1a = -9a
(-5 + -9a + 2a2) = 0

Solving
-5 + -9a + 2a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

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

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

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
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 = {-0.5, 5}