2y=4y^2-6

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

Simplifying
2y = 4y2 + -6

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

Solving
2y = -6 + 4y2

Solving for variable 'y'.

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

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

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

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

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

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

Ignore the factor 2.
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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {1.5, -1}