5b^2=-3-8b

Solution for 5b^2=-3-8b equation:

Simplifying
5b2 = -3 + -8b

Solving
5b2 = -3 + -8b

Solving for variable 'b'.

Reorder the terms:
3 + 8b + 5b2 = -3 + -8b + 3 + 8b

Reorder the terms:
3 + 8b + 5b2 = -3 + 3 + -8b + 8b

Combine like terms: -3 + 3 = 0
3 + 8b + 5b2 = 0 + -8b + 8b
3 + 8b + 5b2 = -8b + 8b

Combine like terms: -8b + 8b = 0
3 + 8b + 5b2 = 0

Factor a trinomial.
(1 + b)(3 + 5b) = 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 '(3 + 5b)' equal to zero and attempt to solve:

Simplifying
3 + 5b = 0

Solving
3 + 5b = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5b = 0 + -3
5b = 0 + -3

Combine like terms: 0 + -3 = -3
5b = -3

Divide each side by '5'.
b = -0.6

Simplifying
b = -0.6
Solution
b = {-1, -0.6}