-4y=2y^2-6

Solution for -4y=2y^2-6 equation:

Simplifying
-4y = 2y2 + -6

Reorder the terms:
-4y = -6 + 2y2

Solving
-4y = -6 + 2y2

Solving for variable 'y'.

Reorder the terms:
6 + -4y + -2y2 = -6 + 2y2 + 6 + -2y2

Reorder the terms:
6 + -4y + -2y2 = -6 + 6 + 2y2 + -2y2

Combine like terms: -6 + 6 = 0
6 + -4y + -2y2 = 0 + 2y2 + -2y2
6 + -4y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
6 + -4y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2y + -1y2) = 0

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

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

Simplifying
1 + -1y = 0

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

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

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

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

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Solution
y = {1, -3}