2y^2-3=-5y

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

Simplifying
2y2 + -3 = -5y

Reorder the terms:
-3 + 2y2 = -5y

Solving
-3 + 2y2 = -5y

Solving for variable 'y'.

Reorder the terms:
-3 + 5y + 2y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
-3 + 5y + 2y2 = 0

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

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 0.5}