3y^2+8y-51=0

Solution for 3y^2+8y-51=0 equation:

Simplifying
3y2 + 8y + -51 = 0

Reorder the terms:
-51 + 8y + 3y2 = 0

Solving
-51 + 8y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-17 + -3y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-17 + -3y)' equal to zero and attempt to solve:

Simplifying
-17 + -3y = 0

Solving
-17 + -3y = 0

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

Add '17' to each side of the equation.
-17 + 17 + -3y = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3y = 0 + 17
-3y = 0 + 17

Combine like terms: 0 + 17 = 17
-3y = 17

Divide each side by '-3'.
y = -5.666666667

Simplifying
y = -5.666666667
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5.666666667, 3}