4b^2+5b=-1

Solution for 4b^2+5b=-1 equation:

Simplifying
4b2 + 5b = -1

Reorder the terms:
5b + 4b2 = -1

Solving
5b + 4b2 = -1

Solving for variable 'b'.

Reorder the terms:
1 + 5b + 4b2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 5b + 4b2 = 0

Factor a trinomial.
(1 + b)(1 + 4b) = 0

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

Simplifying
1 + b = 0

Solving
1 + b = 0

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

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

Combine like terms: 1 + -1 = 0
0 + b = 0 + -1
b = 0 + -1

Combine like terms: 0 + -1 = -1
b = -1

Simplifying
b = -1
Subproblem 2
Set the factor '(1 + 4b)' equal to zero and attempt to solve:

Simplifying
1 + 4b = 0

Solving
1 + 4b = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4b = 0 + -1

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

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

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

Simplifying
b = -0.25
Solution
b = {-1, -0.25}