18y^2+31y+6=0

Solution for 18y^2+31y+6=0 equation:

Simplifying
18y2 + 31y + 6 = 0

Reorder the terms:
6 + 31y + 18y2 = 0

Solving
6 + 31y + 18y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + 2y)(2 + 9y) = 0

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

Simplifying
3 + 2y = 0

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

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(2 + 9y)' equal to zero and attempt to solve:

Simplifying
2 + 9y = 0

Solving
2 + 9y = 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 + 9y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9y = 0 + -2
9y = 0 + -2

Combine like terms: 0 + -2 = -2
9y = -2

Divide each side by '9'.
y = -0.2222222222

Simplifying
y = -0.2222222222
Solution
y = {-1.5, -0.2222222222}