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

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

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

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

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

Multiply (3 + y) * (2 + y)
(3(2 + y) + y(2 + y)) = y(y + 7)
((2 * 3 + y * 3) + y(2 + y)) = y(y + 7)
((6 + 3y) + y(2 + y)) = y(y + 7)
(6 + 3y + (2 * y + y * y)) = y(y + 7)
(6 + 3y + (2y + y2)) = y(y + 7)

Combine like terms: 3y + 2y = 5y
(6 + 5y + y2) = y(y + 7)

Reorder the terms:
6 + 5y + y2 = y(7 + y)
6 + 5y + y2 = (7 * y + y * y)
6 + 5y + y2 = (7y + y2)

Add '-1y2' to each side of the equation.
6 + 5y + y2 + -1y2 = 7y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + 5y + 0 = 7y + y2 + -1y2
6 + 5y = 7y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + 5y = 7y + 0
6 + 5y = 7y

Solving
6 + 5y = 7y

Solving for variable 'y'.

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

Add '-7y' to each side of the equation.
6 + 5y + -7y = 7y + -7y

Combine like terms: 5y + -7y = -2y
6 + -2y = 7y + -7y

Combine like terms: 7y + -7y = 0
6 + -2y = 0

Add '-6' to each side of the equation.
6 + -6 + -2y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2y = 0 + -6
-2y = 0 + -6

Combine like terms: 0 + -6 = -6
-2y = -6

Divide each side by '-2'.
y = 3

Simplifying
y = 3