(y+2)(y-7)-1=(y+1)(y+3)

Solution for (y+2)(y-7)-1=(y+1)(y+3) equation:

Simplifying
(y + 2)(y + -7) + -1 = (y + 1)(y + 3)

Reorder the terms:
(2 + y)(y + -7) + -1 = (y + 1)(y + 3)

Reorder the terms:
(2 + y)(-7 + y) + -1 = (y + 1)(y + 3)

Multiply (2 + y) * (-7 + y)
(2(-7 + y) + y(-7 + y)) + -1 = (y + 1)(y + 3)
((-7 * 2 + y * 2) + y(-7 + y)) + -1 = (y + 1)(y + 3)
((-14 + 2y) + y(-7 + y)) + -1 = (y + 1)(y + 3)
(-14 + 2y + (-7 * y + y * y)) + -1 = (y + 1)(y + 3)
(-14 + 2y + (-7y + y2)) + -1 = (y + 1)(y + 3)

Combine like terms: 2y + -7y = -5y
(-14 + -5y + y2) + -1 = (y + 1)(y + 3)

Reorder the terms:
-14 + -1 + -5y + y2 = (y + 1)(y + 3)

Combine like terms: -14 + -1 = -15
-15 + -5y + y2 = (y + 1)(y + 3)

Reorder the terms:
-15 + -5y + y2 = (1 + y)(y + 3)

Reorder the terms:
-15 + -5y + y2 = (1 + y)(3 + y)

Multiply (1 + y) * (3 + y)
-15 + -5y + y2 = (1(3 + y) + y(3 + y))
-15 + -5y + y2 = ((3 * 1 + y * 1) + y(3 + y))
-15 + -5y + y2 = ((3 + 1y) + y(3 + y))
-15 + -5y + y2 = (3 + 1y + (3 * y + y * y))
-15 + -5y + y2 = (3 + 1y + (3y + y2))

Combine like terms: 1y + 3y = 4y
-15 + -5y + y2 = (3 + 4y + y2)

Add '-1y2' to each side of the equation.
-15 + -5y + y2 + -1y2 = 3 + 4y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + -5y + 0 = 3 + 4y + y2 + -1y2
-15 + -5y = 3 + 4y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + -5y = 3 + 4y + 0
-15 + -5y = 3 + 4y

Solving
-15 + -5y = 3 + 4y

Solving for variable 'y'.

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

Add '-4y' to each side of the equation.
-15 + -5y + -4y = 3 + 4y + -4y

Combine like terms: -5y + -4y = -9y
-15 + -9y = 3 + 4y + -4y

Combine like terms: 4y + -4y = 0
-15 + -9y = 3 + 0
-15 + -9y = 3

Add '15' to each side of the equation.
-15 + 15 + -9y = 3 + 15

Combine like terms: -15 + 15 = 0
0 + -9y = 3 + 15
-9y = 3 + 15

Combine like terms: 3 + 15 = 18
-9y = 18

Divide each side by '-9'.
y = -2

Simplifying
y = -2