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

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

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

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

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

Reorder the terms:
-4 + 6 + 4y + 3y = 5(y + -4)

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

Combine like terms: 4y + 3y = 7y
2 + 7y = 5(y + -4)

Reorder the terms:
2 + 7y = 5(-4 + y)
2 + 7y = (-4 * 5 + y * 5)
2 + 7y = (-20 + 5y)

Solving
2 + 7y = -20 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
2 + 7y + -5y = -20 + 5y + -5y

Combine like terms: 7y + -5y = 2y
2 + 2y = -20 + 5y + -5y

Combine like terms: 5y + -5y = 0
2 + 2y = -20 + 0
2 + 2y = -20

Add '-2' to each side of the equation.
2 + -2 + 2y = -20 + -2

Combine like terms: 2 + -2 = 0
0 + 2y = -20 + -2
2y = -20 + -2

Combine like terms: -20 + -2 = -22
2y = -22

Divide each side by '2'.
y = -11

Simplifying
y = -11