(y+1)(y+5)=(y+2)(y+3)

Solution for (y+1)(y+5)=(y+2)(y+3) equation:

Simplifying
(y + 1)(y + 5) = (y + 2)(y + 3)

Reorder the terms:
(1 + y)(y + 5) = (y + 2)(y + 3)

Reorder the terms:
(1 + y)(5 + y) = (y + 2)(y + 3)

Multiply (1 + y) * (5 + y)
(1(5 + y) + y(5 + y)) = (y + 2)(y + 3)
((5 * 1 + y * 1) + y(5 + y)) = (y + 2)(y + 3)
((5 + 1y) + y(5 + y)) = (y + 2)(y + 3)
(5 + 1y + (5 * y + y * y)) = (y + 2)(y + 3)
(5 + 1y + (5y + y2)) = (y + 2)(y + 3)

Combine like terms: 1y + 5y = 6y
(5 + 6y + y2) = (y + 2)(y + 3)

Reorder the terms:
5 + 6y + y2 = (2 + y)(y + 3)

Reorder the terms:
5 + 6y + y2 = (2 + y)(3 + y)

Multiply (2 + y) * (3 + y)
5 + 6y + y2 = (2(3 + y) + y(3 + y))
5 + 6y + y2 = ((3 * 2 + y * 2) + y(3 + y))
5 + 6y + y2 = ((6 + 2y) + y(3 + y))
5 + 6y + y2 = (6 + 2y + (3 * y + y * y))
5 + 6y + y2 = (6 + 2y + (3y + y2))

Combine like terms: 2y + 3y = 5y
5 + 6y + y2 = (6 + 5y + y2)

Add '-1y2' to each side of the equation.
5 + 6y + y2 + -1y2 = 6 + 5y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5 + 6y + 0 = 6 + 5y + y2 + -1y2
5 + 6y = 6 + 5y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5 + 6y = 6 + 5y + 0
5 + 6y = 6 + 5y

Solving
5 + 6y = 6 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
5 + 6y + -5y = 6 + 5y + -5y

Combine like terms: 6y + -5y = 1y
5 + 1y = 6 + 5y + -5y

Combine like terms: 5y + -5y = 0
5 + 1y = 6 + 0
5 + 1y = 6

Add '-5' to each side of the equation.
5 + -5 + 1y = 6 + -5

Combine like terms: 5 + -5 = 0
0 + 1y = 6 + -5
1y = 6 + -5

Combine like terms: 6 + -5 = 1
1y = 1

Divide each side by '1'.
y = 1

Simplifying
y = 1