y^2+4y+6y+24=0

Solution for y^2+4y+6y+24=0 equation:

Simplifying
y2 + 4y + 6y + 24 = 0

Reorder the terms:
24 + 4y + 6y + y2 = 0

Combine like terms: 4y + 6y = 10y
24 + 10y + y2 = 0

Solving
24 + 10y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(4 + y) = 0

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

Simplifying
6 + y = 0

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

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

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

Simplifying
y = -6
Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {-6, -4}