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

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

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

Reorder the terms:
5(-2 + y) + 2(y + 1) = 3(y + -6)
(-2 * 5 + y * 5) + 2(y + 1) = 3(y + -6)
(-10 + 5y) + 2(y + 1) = 3(y + -6)

Reorder the terms:
-10 + 5y + 2(1 + y) = 3(y + -6)
-10 + 5y + (1 * 2 + y * 2) = 3(y + -6)
-10 + 5y + (2 + 2y) = 3(y + -6)

Reorder the terms:
-10 + 2 + 5y + 2y = 3(y + -6)

Combine like terms: -10 + 2 = -8
-8 + 5y + 2y = 3(y + -6)

Combine like terms: 5y + 2y = 7y
-8 + 7y = 3(y + -6)

Reorder the terms:
-8 + 7y = 3(-6 + y)
-8 + 7y = (-6 * 3 + y * 3)
-8 + 7y = (-18 + 3y)

Solving
-8 + 7y = -18 + 3y

Solving for variable 'y'.

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

Add '-3y' to each side of the equation.
-8 + 7y + -3y = -18 + 3y + -3y

Combine like terms: 7y + -3y = 4y
-8 + 4y = -18 + 3y + -3y

Combine like terms: 3y + -3y = 0
-8 + 4y = -18 + 0
-8 + 4y = -18

Add '8' to each side of the equation.
-8 + 8 + 4y = -18 + 8

Combine like terms: -8 + 8 = 0
0 + 4y = -18 + 8
4y = -18 + 8

Combine like terms: -18 + 8 = -10
4y = -10

Divide each side by '4'.
y = -2.5

Simplifying
y = -2.5