4s(s+1)=-1

Solution for 4s(s+1)=-1 equation:

Simplifying
4s(s + 1) = -1

Reorder the terms:
4s(1 + s) = -1
(1 * 4s + s * 4s) = -1
(4s + 4s2) = -1

Solving
4s + 4s2 = -1

Solving for variable 's'.

Reorder the terms:
1 + 4s + 4s2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 4s + 4s2 = 0

Factor a trinomial.
(1 + 2s)(1 + 2s) = 0

Subproblem 1
Set the factor '(1 + 2s)' equal to zero and attempt to solve:

Simplifying
1 + 2s = 0

Solving
1 + 2s = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2s = 0 + -1
2s = 0 + -1

Combine like terms: 0 + -1 = -1
2s = -1

Divide each side by '2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
Set the factor '(1 + 2s)' equal to zero and attempt to solve:

Simplifying
1 + 2s = 0

Solving
1 + 2s = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2s = 0 + -1
2s = 0 + -1

Combine like terms: 0 + -1 = -1
2s = -1

Divide each side by '2'.
s = -0.5

Simplifying
s = -0.5
Solution
s = {-0.5, -0.5}