(y+1)(y-3)=5

Solution for (y+1)(y-3)=5 equation:

Simplifying
(y + 1)(y + -3) = 5

Reorder the terms:
(1 + y)(y + -3) = 5

Reorder the terms:
(1 + y)(-3 + y) = 5

Multiply (1 + y) * (-3 + y)
(1(-3 + y) + y(-3 + y)) = 5
((-3 * 1 + y * 1) + y(-3 + y)) = 5
((-3 + 1y) + y(-3 + y)) = 5
(-3 + 1y + (-3 * y + y * y)) = 5
(-3 + 1y + (-3y + y2)) = 5

Combine like terms: 1y + -3y = -2y
(-3 + -2y + y2) = 5

Solving
-3 + -2y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-3 + -5 + -2y + y2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -2y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -2y + y2 = 0

Factor a trinomial.
(-2 + -1y)(4 + -1y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-2, 4}