6y^2=y+1

Solution for 6y^2=y+1 equation:

Simplifying
6y2 = y + 1

Reorder the terms:
6y2 = 1 + y

Solving
6y2 = 1 + y

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 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 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3y = 0 + 1
-3y = 0 + 1

Combine like terms: 0 + 1 = 1
-3y = 1

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
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 = {-0.3333333333, 0.5}