3y^2+20y+17=0

Solution for 3y^2+20y+17=0 equation:

Simplifying
3y2 + 20y + 17 = 0

Reorder the terms:
17 + 20y + 3y2 = 0

Solving
17 + 20y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(17 + 3y)(1 + y) = 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 '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {-5.666666667, -1}