6y^2=-13y-6

Solution for 6y^2=-13y-6 equation:

Simplifying
6y2 = -13y + -6

Reorder the terms:
6y2 = -6 + -13y

Solving
6y2 = -6 + -13y

Solving for variable 'y'.

Reorder the terms:
6 + 13y + 6y2 = -6 + -13y + 6 + 13y

Reorder the terms:
6 + 13y + 6y2 = -6 + 6 + -13y + 13y

Combine like terms: -6 + 6 = 0
6 + 13y + 6y2 = 0 + -13y + 13y
6 + 13y + 6y2 = -13y + 13y

Combine like terms: -13y + 13y = 0
6 + 13y + 6y2 = 0

Factor a trinomial.
(3 + 2y)(2 + 3y) = 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 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

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

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

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

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-1.5, -0.6666666667}