6y^2+19y+3=0

Solution for 6y^2+19y+3=0 equation:

Simplifying
6y2 + 19y + 3 = 0

Reorder the terms:
3 + 19y + 6y2 = 0

Solving
3 + 19y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(1 + 6y) = 0

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Subproblem 2
Set the factor '(1 + 6y)' equal to zero and attempt to solve:

Simplifying
1 + 6y = 0

Solving
1 + 6y = 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 + 6y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6y = 0 + -1
6y = 0 + -1

Combine like terms: 0 + -1 = -1
6y = -1

Divide each side by '6'.
y = -0.1666666667

Simplifying
y = -0.1666666667
Solution
y = {-3, -0.1666666667}