4z-(z+6)=6y-3(y-3)

Solution for 4z-(z+6)=6y-3(y-3) equation:

Simplifying
4z + -1(z + 6) = 6y + -3(y + -3)

Reorder the terms:
4z + -1(6 + z) = 6y + -3(y + -3)
4z + (6 * -1 + z * -1) = 6y + -3(y + -3)
4z + (-6 + -1z) = 6y + -3(y + -3)

Reorder the terms:
-6 + 4z + -1z = 6y + -3(y + -3)

Combine like terms: 4z + -1z = 3z
-6 + 3z = 6y + -3(y + -3)

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

Reorder the terms:
-6 + 3z = 9 + 6y + -3y

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

Solving
-6 + 3z = 9 + 3y

Solving for variable 'z'.

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

Add '6' to each side of the equation.
-6 + 6 + 3z = 9 + 6 + 3y

Combine like terms: -6 + 6 = 0
0 + 3z = 9 + 6 + 3y
3z = 9 + 6 + 3y

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

Divide each side by '3'.
z = 5 + y

Simplifying
z = 5 + y