2y(y+1)-3(y-2)=5y+8-6y

Solution for 2y(y+1)-3(y-2)=5y+8-6y equation:

Simplifying
2y(y + 1) + -3(y + -2) = 5y + 8 + -6y

Reorder the terms:
2y(1 + y) + -3(y + -2) = 5y + 8 + -6y
(1 * 2y + y * 2y) + -3(y + -2) = 5y + 8 + -6y
(2y + 2y2) + -3(y + -2) = 5y + 8 + -6y

Reorder the terms:
2y + 2y2 + -3(-2 + y) = 5y + 8 + -6y
2y + 2y2 + (-2 * -3 + y * -3) = 5y + 8 + -6y
2y + 2y2 + (6 + -3y) = 5y + 8 + -6y

Reorder the terms:
6 + 2y + -3y + 2y2 = 5y + 8 + -6y

Combine like terms: 2y + -3y = -1y
6 + -1y + 2y2 = 5y + 8 + -6y

Reorder the terms:
6 + -1y + 2y2 = 8 + 5y + -6y

Combine like terms: 5y + -6y = -1y
6 + -1y + 2y2 = 8 + -1y

Add 'y' to each side of the equation.
6 + -1y + y + 2y2 = 8 + -1y + y

Combine like terms: -1y + y = 0
6 + 0 + 2y2 = 8 + -1y + y
6 + 2y2 = 8 + -1y + y

Combine like terms: -1y + y = 0
6 + 2y2 = 8 + 0
6 + 2y2 = 8

Solving
6 + 2y2 = 8

Solving for variable 'y'.

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

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

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

Combine like terms: 8 + -6 = 2
2y2 = 2

Divide each side by '2'.
y2 = 1

Simplifying
y2 = 1

Take the square root of each side:
y = {-1, 1}