12y^2=1-y

Solution for 12y^2=1-y equation:

Simplifying
12y2 = 1 + -1y

Solving
12y2 = 1 + -1y

Solving for variable 'y'.

Reorder the terms:
-1 + y + 12y2 = 1 + -1y + -1 + y

Reorder the terms:
-1 + y + 12y2 = 1 + -1 + -1y + y

Combine like terms: 1 + -1 = 0
-1 + y + 12y2 = 0 + -1y + y
-1 + y + 12y2 = -1y + y

Combine like terms: -1y + y = 0
-1 + y + 12y2 = 0

Factor a trinomial.
(-1 + -3y)(1 + -4y) = 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 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y = 0 + -1
-4y = 0 + -1

Combine like terms: 0 + -1 = -1
-4y = -1

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Solution
y = {-0.3333333333, 0.25}