(y+1)(3y+3)=48

Solution for (y+1)(3y+3)=48 equation:

Simplifying
(y + 1)(3y + 3) = 48

Reorder the terms:
(1 + y)(3y + 3) = 48

Reorder the terms:
(1 + y)(3 + 3y) = 48

Multiply (1 + y) * (3 + 3y)
(1(3 + 3y) + y(3 + 3y)) = 48
((3 * 1 + 3y * 1) + y(3 + 3y)) = 48
((3 + 3y) + y(3 + 3y)) = 48
(3 + 3y + (3 * y + 3y * y)) = 48
(3 + 3y + (3y + 3y2)) = 48

Combine like terms: 3y + 3y = 6y
(3 + 6y + 3y2) = 48

Solving
3 + 6y + 3y2 = 48

Solving for variable 'y'.

Reorder the terms:
3 + -48 + 6y + 3y2 = 48 + -48

Combine like terms: 3 + -48 = -45
-45 + 6y + 3y2 = 48 + -48

Combine like terms: 48 + -48 = 0
-45 + 6y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2y + y2) = 0

Factor a trinomial.
3((-5 + -1y)(3 + -1y)) = 0

Ignore the factor 3.
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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

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