2(y+1)(y+3)=16

Solution for 2(y+1)(y+3)=16 equation:

Simplifying
2(y + 1)(y + 3) = 16

Reorder the terms:
2(1 + y)(y + 3) = 16

Reorder the terms:
2(1 + y)(3 + y) = 16

Multiply (1 + y) * (3 + y)
2(1(3 + y) + y(3 + y)) = 16
2((3 * 1 + y * 1) + y(3 + y)) = 16
2((3 + 1y) + y(3 + y)) = 16
2(3 + 1y + (3 * y + y * y)) = 16
2(3 + 1y + (3y + y2)) = 16

Combine like terms: 1y + 3y = 4y
2(3 + 4y + y2) = 16
(3 * 2 + 4y * 2 + y2 * 2) = 16
(6 + 8y + 2y2) = 16

Solving
6 + 8y + 2y2 = 16

Solving for variable 'y'.

Reorder the terms:
6 + -16 + 8y + 2y2 = 16 + -16

Combine like terms: 6 + -16 = -10
-10 + 8y + 2y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-10 + 8y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4y + y2) = 0

Factor a trinomial.
2((-5 + -1y)(1 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 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 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-5, 1}