0=y^2+5y+6

Solution for 0=y^2+5y+6 equation:

Simplifying
0 = y2 + 5y + 6

Reorder the terms:
0 = 6 + 5y + y2

Solving
0 = 6 + 5y + y2

Solving for variable 'y'.

Combine like terms: 0 + -6 = -6
-6 + -5y + -1y2 = 6 + 5y + y2 + -6 + -5y + -1y2

Reorder the terms:
-6 + -5y + -1y2 = 6 + -6 + 5y + -5y + y2 + -1y2

Combine like terms: 6 + -6 = 0
-6 + -5y + -1y2 = 0 + 5y + -5y + y2 + -1y2
-6 + -5y + -1y2 = 5y + -5y + y2 + -1y2

Combine like terms: 5y + -5y = 0
-6 + -5y + -1y2 = 0 + y2 + -1y2
-6 + -5y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-6 + -5y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5y + y2) = 0

Factor a trinomial.
-1((3 + y)(2 + y)) = 0

Ignore the factor -1.
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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {-3, -2}