y^2+22y+42=-54

Solution for y^2+22y+42=-54 equation:

Simplifying
y2 + 22y + 42 = -54

Reorder the terms:
42 + 22y + y2 = -54

Solving
42 + 22y + y2 = -54

Solving for variable 'y'.

Reorder the terms:
42 + 54 + 22y + y2 = -54 + 54

Combine like terms: 42 + 54 = 96
96 + 22y + y2 = -54 + 54

Combine like terms: -54 + 54 = 0
96 + 22y + y2 = 0

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

Subproblem 1
Set the factor '(16 + y)' equal to zero and attempt to solve:

Simplifying
16 + y = 0

Solving
16 + y = 0

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

Add '-16' to each side of the equation.
16 + -16 + y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + y = 0 + -16
y = 0 + -16

Combine like terms: 0 + -16 = -16
y = -16

Simplifying
y = -16
Subproblem 2
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
Solution
y = {-16, -6}