7y^2+17y+6=0

Solution for 7y^2+17y+6=0 equation:

Simplifying
7y2 + 17y + 6 = 0

Reorder the terms:
6 + 17y + 7y2 = 0

Solving
6 + 17y + 7y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + y)(3 + 7y) = 0

Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(3 + 7y)' equal to zero and attempt to solve:

Simplifying
3 + 7y = 0

Solving
3 + 7y = 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 + 7y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7y = 0 + -3
7y = 0 + -3

Combine like terms: 0 + -3 = -3
7y = -3

Divide each side by '7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
Solution
y = {-2, -0.4285714286}