7y^2+13y+6=0

Solution for 7y^2+13y+6=0 equation:

Simplifying
7y2 + 13y + 6 = 0

Reorder the terms:
6 + 13y + 7y2 = 0

Solving
6 + 13y + 7y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + y)(6 + 7y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + 7y)' equal to zero and attempt to solve:

Simplifying
6 + 7y = 0

Solving
6 + 7y = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7y = 0 + -6
7y = 0 + -6

Combine like terms: 0 + -6 = -6
7y = -6

Divide each side by '7'.
y = -0.8571428571

Simplifying
y = -0.8571428571
Solution
y = {-1, -0.8571428571}