5y^2=-8y-3

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

Simplifying
5y2 = -8y + -3

Reorder the terms:
5y2 = -3 + -8y

Solving
5y2 = -3 + -8y

Solving for variable 'y'.

Reorder the terms:
3 + 8y + 5y2 = -3 + -8y + 3 + 8y

Reorder the terms:
3 + 8y + 5y2 = -3 + 3 + -8y + 8y

Combine like terms: -3 + 3 = 0
3 + 8y + 5y2 = 0 + -8y + 8y
3 + 8y + 5y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
3 + 8y + 5y2 = 0

Factor a trinomial.
(1 + y)(3 + 5y) = 0

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 0

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

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

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

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

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

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