(2y+1)(y+6)=2y(y+4)+81

Solution for (2y+1)(y+6)=2y(y+4)+81 equation:

Simplifying
(2y + 1)(y + 6) = 2y(y + 4) + 81

Reorder the terms:
(1 + 2y)(y + 6) = 2y(y + 4) + 81

Reorder the terms:
(1 + 2y)(6 + y) = 2y(y + 4) + 81

Multiply (1 + 2y) * (6 + y)
(1(6 + y) + 2y * (6 + y)) = 2y(y + 4) + 81
((6 * 1 + y * 1) + 2y * (6 + y)) = 2y(y + 4) + 81
((6 + 1y) + 2y * (6 + y)) = 2y(y + 4) + 81
(6 + 1y + (6 * 2y + y * 2y)) = 2y(y + 4) + 81
(6 + 1y + (12y + 2y2)) = 2y(y + 4) + 81

Combine like terms: 1y + 12y = 13y
(6 + 13y + 2y2) = 2y(y + 4) + 81

Reorder the terms:
6 + 13y + 2y2 = 2y(4 + y) + 81
6 + 13y + 2y2 = (4 * 2y + y * 2y) + 81
6 + 13y + 2y2 = (8y + 2y2) + 81

Reorder the terms:
6 + 13y + 2y2 = 81 + 8y + 2y2

Add '-2y2' to each side of the equation.
6 + 13y + 2y2 + -2y2 = 81 + 8y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
6 + 13y + 0 = 81 + 8y + 2y2 + -2y2
6 + 13y = 81 + 8y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
6 + 13y = 81 + 8y + 0
6 + 13y = 81 + 8y

Solving
6 + 13y = 81 + 8y

Solving for variable 'y'.

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

Add '-8y' to each side of the equation.
6 + 13y + -8y = 81 + 8y + -8y

Combine like terms: 13y + -8y = 5y
6 + 5y = 81 + 8y + -8y

Combine like terms: 8y + -8y = 0
6 + 5y = 81 + 0
6 + 5y = 81

Add '-6' to each side of the equation.
6 + -6 + 5y = 81 + -6

Combine like terms: 6 + -6 = 0
0 + 5y = 81 + -6
5y = 81 + -6

Combine like terms: 81 + -6 = 75
5y = 75

Divide each side by '5'.
y = 15

Simplifying
y = 15