2(y-2)+5(2-y)=-3(2y+2)

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

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

Reorder the terms:
2(-2 + y) + 5(2 + -1y) = -3(2y + 2)
(-2 * 2 + y * 2) + 5(2 + -1y) = -3(2y + 2)
(-4 + 2y) + 5(2 + -1y) = -3(2y + 2)
-4 + 2y + (2 * 5 + -1y * 5) = -3(2y + 2)
-4 + 2y + (10 + -5y) = -3(2y + 2)

Reorder the terms:
-4 + 10 + 2y + -5y = -3(2y + 2)

Combine like terms: -4 + 10 = 6
6 + 2y + -5y = -3(2y + 2)

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

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

Solving
6 + -3y = -6 + -6y

Solving for variable 'y'.

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

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

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

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

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

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

Combine like terms: -6 + -6 = -12
3y = -12

Divide each side by '3'.
y = -4

Simplifying
y = -4