3y^2-2y-8=0

Solution for 3y^2-2y-8=0 equation:

Simplifying
3y2 + -2y + -8 = 0

Reorder the terms:
-8 + -2y + 3y2 = 0

Solving
-8 + -2y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -3y)(2 + -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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

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