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

Solution for (2a-1)(a+5)= 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.
(-5 + -1a)(1 + -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 '(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
Solution
a = {-5, 0.5}