2Y^2+2=-5Y

Solution for 2Y^2+2=-5Y equation:

Simplifying
2Y2 + 2 = -5Y

Reorder the terms:
2 + 2Y2 = -5Y

Solving
2 + 2Y2 = -5Y

Solving for variable 'Y'.

Reorder the terms:
2 + 5Y + 2Y2 = -5Y + 5Y

Combine like terms: -5Y + 5Y = 0
2 + 5Y + 2Y2 = 0

Factor a trinomial.
(2 + Y)(1 + 2Y) = 0

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

Simplifying
2 + Y = 0

Solving
2 + Y = 0

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

Add '-2' to each side of the equation.
2 + -2 + Y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + Y = 0 + -2
Y = 0 + -2

Combine like terms: 0 + -2 = -2
Y = -2

Simplifying
Y = -2
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 = {-2, -0.5}