(a+5)(4a-1)=0

Solution for (a+5)(4a-1)=0 equation:

Simplifying
(a + 5)(4a + -1) = 0

Reorder the terms:
(5 + a)(4a + -1) = 0

Reorder the terms:
(5 + a)(-1 + 4a) = 0

Multiply (5 + a) * (-1 + 4a)
(5(-1 + 4a) + a(-1 + 4a)) = 0
((-1 * 5 + 4a * 5) + a(-1 + 4a)) = 0
((-5 + 20a) + a(-1 + 4a)) = 0
(-5 + 20a + (-1 * a + 4a * a)) = 0
(-5 + 20a + (-1a + 4a2)) = 0

Combine like terms: 20a + -1a = 19a
(-5 + 19a + 4a2) = 0

Solving
-5 + 19a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(1 + -4a) = 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 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {-5, 0.25}