3y+4(y-8)=8y-3(y-10)

Solution for 3y+4(y-8)=8y-3(y-10) equation:

Simplifying
3y + 4(y + -8) = 8y + -3(y + -10)

Reorder the terms:
3y + 4(-8 + y) = 8y + -3(y + -10)
3y + (-8 * 4 + y * 4) = 8y + -3(y + -10)
3y + (-32 + 4y) = 8y + -3(y + -10)

Reorder the terms:
-32 + 3y + 4y = 8y + -3(y + -10)

Combine like terms: 3y + 4y = 7y
-32 + 7y = 8y + -3(y + -10)

Reorder the terms:
-32 + 7y = 8y + -3(-10 + y)
-32 + 7y = 8y + (-10 * -3 + y * -3)
-32 + 7y = 8y + (30 + -3y)

Reorder the terms:
-32 + 7y = 30 + 8y + -3y

Combine like terms: 8y + -3y = 5y
-32 + 7y = 30 + 5y

Solving
-32 + 7y = 30 + 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.
-32 + 7y + -5y = 30 + 5y + -5y

Combine like terms: 7y + -5y = 2y
-32 + 2y = 30 + 5y + -5y

Combine like terms: 5y + -5y = 0
-32 + 2y = 30 + 0
-32 + 2y = 30

Add '32' to each side of the equation.
-32 + 32 + 2y = 30 + 32

Combine like terms: -32 + 32 = 0
0 + 2y = 30 + 32
2y = 30 + 32

Combine like terms: 30 + 32 = 62
2y = 62

Divide each side by '2'.
y = 31

Simplifying
y = 31