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

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

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

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

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

Combine like terms: 3y + 1y = 4y
(3 + 4y + y2) = (y + 1)(y + -1)

Reorder the terms:
3 + 4y + y2 = (1 + y)(y + -1)

Reorder the terms:
3 + 4y + y2 = (1 + y)(-1 + y)

Multiply (1 + y) * (-1 + y)
3 + 4y + y2 = (1(-1 + y) + y(-1 + y))
3 + 4y + y2 = ((-1 * 1 + y * 1) + y(-1 + y))
3 + 4y + y2 = ((-1 + 1y) + y(-1 + y))
3 + 4y + y2 = (-1 + 1y + (-1 * y + y * y))
3 + 4y + y2 = (-1 + 1y + (-1y + y2))

Combine like terms: 1y + -1y = 0
3 + 4y + y2 = (-1 + 0 + y2)
3 + 4y + y2 = (-1 + y2)

Add '-1y2' to each side of the equation.
3 + 4y + y2 + -1y2 = -1 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
3 + 4y + 0 = -1 + y2 + -1y2
3 + 4y = -1 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
3 + 4y = -1 + 0
3 + 4y = -1

Solving
3 + 4y = -1

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + 4y = -1 + -3

Combine like terms: 3 + -3 = 0
0 + 4y = -1 + -3
4y = -1 + -3

Combine like terms: -1 + -3 = -4
4y = -4

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

Simplifying
y = -1