y^2+24y+38=-42

Solution for y^2+24y+38=-42 equation:

Simplifying
y2 + 24y + 38 = -42

Reorder the terms:
38 + 24y + y2 = -42

Solving
38 + 24y + y2 = -42

Solving for variable 'y'.

Reorder the terms:
38 + 42 + 24y + y2 = -42 + 42

Combine like terms: 38 + 42 = 80
80 + 24y + y2 = -42 + 42

Combine like terms: -42 + 42 = 0
80 + 24y + y2 = 0

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

Subproblem 1
Set the factor '(20 + y)' equal to zero and attempt to solve:

Simplifying
20 + y = 0

Solving
20 + y = 0

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

Add '-20' to each side of the equation.
20 + -20 + y = 0 + -20

Combine like terms: 20 + -20 = 0
0 + y = 0 + -20
y = 0 + -20

Combine like terms: 0 + -20 = -20
y = -20

Simplifying
y = -20
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 = {-20, -4}