2=y+6y^2

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

Simplifying
2 = y + 6y2

Solving
2 = y + 6y2

Solving for variable 'y'.

Reorder the terms:
2 + -1y + -6y2 = y + -1y + 6y2 + -6y2

Combine like terms: y + -1y = 0
2 + -1y + -6y2 = 0 + 6y2 + -6y2
2 + -1y + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
2 + -1y + -6y2 = 0

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

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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

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

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

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {0.5, -0.6666666667}