3y+4(y-8)=7y-2(y-10)

Solution for 3y+4(y-8)=7y-2(y-10) equation:

Simplifying
3y + 4(y + -8) = 7y + -2(y + -10)

Reorder the terms:
3y + 4(-8 + y) = 7y + -2(y + -10)
3y + (-8 * 4 + y * 4) = 7y + -2(y + -10)
3y + (-32 + 4y) = 7y + -2(y + -10)

Reorder the terms:
-32 + 3y + 4y = 7y + -2(y + -10)

Combine like terms: 3y + 4y = 7y
-32 + 7y = 7y + -2(y + -10)

Reorder the terms:
-32 + 7y = 7y + -2(-10 + y)
-32 + 7y = 7y + (-10 * -2 + y * -2)
-32 + 7y = 7y + (20 + -2y)

Reorder the terms:
-32 + 7y = 20 + 7y + -2y

Combine like terms: 7y + -2y = 5y
-32 + 7y = 20 + 5y

Solving
-32 + 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.
-32 + 7y + -5y = 20 + 5y + -5y

Combine like terms: 7y + -5y = 2y
-32 + 2y = 20 + 5y + -5y

Combine like terms: 5y + -5y = 0
-32 + 2y = 20 + 0
-32 + 2y = 20

Add '32' to each side of the equation.
-32 + 32 + 2y = 20 + 32

Combine like terms: -32 + 32 = 0
0 + 2y = 20 + 32
2y = 20 + 32

Combine like terms: 20 + 32 = 52
2y = 52

Divide each side by '2'.
y = 26

Simplifying
y = 26