2y^2+6=-7y

Solution for 2y^2+6=-7y equation:

Simplifying
2y2 + 6 = -7y

Reorder the terms:
6 + 2y2 = -7y

Solving
6 + 2y2 = -7y

Solving for variable 'y'.

Reorder the terms:
6 + 7y + 2y2 = -7y + 7y

Combine like terms: -7y + 7y = 0
6 + 7y + 2y2 = 0

Factor a trinomial.
(2 + y)(3 + 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 '(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
Solution
y = {-2, -1.5}