(y+5)(y+1)=21

Solution for (y+5)(y+1)=21 equation:

Simplifying
(y + 5)(y + 1) = 21

Reorder the terms:
(5 + y)(y + 1) = 21

Reorder the terms:
(5 + y)(1 + y) = 21

Multiply (5 + y) * (1 + y)
(5(1 + y) + y(1 + y)) = 21
((1 * 5 + y * 5) + y(1 + y)) = 21
((5 + 5y) + y(1 + y)) = 21
(5 + 5y + (1 * y + y * y)) = 21
(5 + 5y + (1y + y2)) = 21

Combine like terms: 5y + 1y = 6y
(5 + 6y + y2) = 21

Solving
5 + 6y + y2 = 21

Solving for variable 'y'.

Reorder the terms:
5 + -21 + 6y + y2 = 21 + -21

Combine like terms: 5 + -21 = -16
-16 + 6y + y2 = 21 + -21

Combine like terms: 21 + -21 = 0
-16 + 6y + y2 = 0

Factor a trinomial.
(-8 + -1y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-8, 2}