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

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

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

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

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

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

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

Solving
-1 + 4a + 5a2 = 0

Solving for variable 'a'.

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

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
Solution
a = {-1, 0.2}