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

Solution for 4(y-1)+5(y+2)=3(y-5) equation:

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

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

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

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

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

Combine like terms: 4y + 5y = 9y
6 + 9y = 3(y + -5)

Reorder the terms:
6 + 9y = 3(-5 + y)
6 + 9y = (-5 * 3 + y * 3)
6 + 9y = (-15 + 3y)

Solving
6 + 9y = -15 + 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.
6 + 9y + -3y = -15 + 3y + -3y

Combine like terms: 9y + -3y = 6y
6 + 6y = -15 + 3y + -3y

Combine like terms: 3y + -3y = 0
6 + 6y = -15 + 0
6 + 6y = -15

Add '-6' to each side of the equation.
6 + -6 + 6y = -15 + -6

Combine like terms: 6 + -6 = 0
0 + 6y = -15 + -6
6y = -15 + -6

Combine like terms: -15 + -6 = -21
6y = -21

Divide each side by '6'.
y = -3.5

Simplifying
y = -3.5