6y^2+19y+13=0

Solution for 6y^2+19y+13=0 equation:

Simplifying
6y2 + 19y + 13 = 0

Reorder the terms:
13 + 19y + 6y2 = 0

Solving
13 + 19y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(13 + 6y)(1 + y) = 0

Subproblem 1
Set the factor '(13 + 6y)' equal to zero and attempt to solve:

Simplifying
13 + 6y = 0

Solving
13 + 6y = 0

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

Add '-13' to each side of the equation.
13 + -13 + 6y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 6y = 0 + -13
6y = 0 + -13

Combine like terms: 0 + -13 = -13
6y = -13

Divide each side by '6'.
y = -2.166666667

Simplifying
y = -2.166666667
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 = {-2.166666667, -1}