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

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

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

Reorder the terms:
4(-5 + y) + 2(y + -2) = 3(y + -3)
(-5 * 4 + y * 4) + 2(y + -2) = 3(y + -3)
(-20 + 4y) + 2(y + -2) = 3(y + -3)

Reorder the terms:
-20 + 4y + 2(-2 + y) = 3(y + -3)
-20 + 4y + (-2 * 2 + y * 2) = 3(y + -3)
-20 + 4y + (-4 + 2y) = 3(y + -3)

Reorder the terms:
-20 + -4 + 4y + 2y = 3(y + -3)

Combine like terms: -20 + -4 = -24
-24 + 4y + 2y = 3(y + -3)

Combine like terms: 4y + 2y = 6y
-24 + 6y = 3(y + -3)

Reorder the terms:
-24 + 6y = 3(-3 + y)
-24 + 6y = (-3 * 3 + y * 3)
-24 + 6y = (-9 + 3y)

Solving
-24 + 6y = -9 + 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.
-24 + 6y + -3y = -9 + 3y + -3y

Combine like terms: 6y + -3y = 3y
-24 + 3y = -9 + 3y + -3y

Combine like terms: 3y + -3y = 0
-24 + 3y = -9 + 0
-24 + 3y = -9

Add '24' to each side of the equation.
-24 + 24 + 3y = -9 + 24

Combine like terms: -24 + 24 = 0
0 + 3y = -9 + 24
3y = -9 + 24

Combine like terms: -9 + 24 = 15
3y = 15

Divide each side by '3'.
y = 5

Simplifying
y = 5