3y^2=-y+4

Solution for 3y^2=-y+4 equation:

Simplifying
3y2 = -1y + 4

Reorder the terms:
3y2 = 4 + -1y

Solving
3y2 = 4 + -1y

Solving for variable 'y'.

Reorder the terms:
-4 + y + 3y2 = 4 + -1y + -4 + y

Reorder the terms:
-4 + y + 3y2 = 4 + -4 + -1y + y

Combine like terms: 4 + -4 = 0
-4 + y + 3y2 = 0 + -1y + y
-4 + y + 3y2 = -1y + y

Combine like terms: -1y + y = 0
-4 + y + 3y2 = 0

Factor a trinomial.
(-4 + -3y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y = 0 + 4
-3y = 0 + 4

Combine like terms: 0 + 4 = 4
-3y = 4

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333
Subproblem 2
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
Solution
y = {-1.333333333, 1}