4y^2+3=-8y

Solution for 4y^2+3=-8y equation:

Simplifying
4y2 + 3 = -8y

Reorder the terms:
3 + 4y2 = -8y

Solving
3 + 4y2 = -8y

Solving for variable 'y'.

Reorder the terms:
3 + 8y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
3 + 8y + 4y2 = 0

Factor a trinomial.
(3 + 2y)(1 + 2y) = 0

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

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

Simplifying
y = -0.5
Solution
y = {-1.5, -0.5}