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

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

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

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

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

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

Combine like terms: 1a + -10a = -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}