5a(5a+2)=-1

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

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

Reorder the terms:
5a(2 + 5a) = -1
(2 * 5a + 5a * 5a) = -1
(10a + 25a2) = -1

Solving
10a + 25a2 = -1

Solving for variable 'a'.

Reorder the terms:
1 + 10a + 25a2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 10a + 25a2 = 0

Factor a trinomial.
(1 + 5a)(1 + 5a) = 0

Subproblem 1
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
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 = {-0.2, -0.2}