a(5a+1)=0

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

Simplifying
a(5a + 1) = 0

Reorder the terms:
a(1 + 5a) = 0
(1 * a + 5a * a) = 0
(1a + 5a2) = 0

Solving
1a + 5a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + 5a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
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 = {0, -0.2}