y^2+8y+21=6

Solution for y^2+8y+21=6 equation:

Simplifying
y2 + 8y + 21 = 6

Reorder the terms:
21 + 8y + y2 = 6

Solving
21 + 8y + y2 = 6

Solving for variable 'y'.

Reorder the terms:
21 + -6 + 8y + y2 = 6 + -6

Combine like terms: 21 + -6 = 15
15 + 8y + y2 = 6 + -6

Combine like terms: 6 + -6 = 0
15 + 8y + y2 = 0

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

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
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 = {-5, -3}