y^2+20y+84=0

Solution for y^2+20y+84=0 equation:

Simplifying
y2 + 20y + 84 = 0

Reorder the terms:
84 + 20y + y2 = 0

Solving
84 + 20y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(14 + y)' equal to zero and attempt to solve:

Simplifying
14 + y = 0

Solving
14 + y = 0

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

Add '-14' to each side of the equation.
14 + -14 + y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + y = 0 + -14
y = 0 + -14

Combine like terms: 0 + -14 = -14
y = -14

Simplifying
y = -14
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 = {-14, -6}