y^2+21y+54=0

Solution for y^2+21y+54=0 equation:

Simplifying
y2 + 21y + 54 = 0

Reorder the terms:
54 + 21y + y2 = 0

Solving
54 + 21y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(18 + y)(3 + y) = 0

Subproblem 1
Set the factor '(18 + y)' equal to zero and attempt to solve:

Simplifying
18 + y = 0

Solving
18 + y = 0

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

Add '-18' to each side of the equation.
18 + -18 + y = 0 + -18

Combine like terms: 18 + -18 = 0
0 + y = 0 + -18
y = 0 + -18

Combine like terms: 0 + -18 = -18
y = -18

Simplifying
y = -18
Subproblem 2
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
Solution
y = {-18, -3}