2y(y-4)+6=2(y^2-3y)-5y

Solution for 2y(y-4)+6=2(y^2-3y)-5y equation:

Simplifying
2y(y + -4) + 6 = 2(y2 + -3y) + -5y

Reorder the terms:
2y(-4 + y) + 6 = 2(y2 + -3y) + -5y
(-4 * 2y + y * 2y) + 6 = 2(y2 + -3y) + -5y
(-8y + 2y2) + 6 = 2(y2 + -3y) + -5y

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

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

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

Combine like terms: -6y + -5y = -11y
6 + -8y + 2y2 = -11y + 2y2

Add '-2y2' to each side of the equation.
6 + -8y + 2y2 + -2y2 = -11y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
6 + -8y + 0 = -11y + 2y2 + -2y2
6 + -8y = -11y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
6 + -8y = -11y + 0
6 + -8y = -11y

Solving
6 + -8y = -11y

Solving for variable 'y'.

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

Add '11y' to each side of the equation.
6 + -8y + 11y = -11y + 11y

Combine like terms: -8y + 11y = 3y
6 + 3y = -11y + 11y

Combine like terms: -11y + 11y = 0
6 + 3y = 0

Add '-6' to each side of the equation.
6 + -6 + 3y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 3y = 0 + -6
3y = 0 + -6

Combine like terms: 0 + -6 = -6
3y = -6

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

Simplifying
y = -2