3z+3(z-2)=7z-3(z-10)

Solution for 3z+3(z-2)=7z-3(z-10) equation:

Simplifying
3z + 3(z + -2) = 7z + -3(z + -10)

Reorder the terms:
3z + 3(-2 + z) = 7z + -3(z + -10)
3z + (-2 * 3 + z * 3) = 7z + -3(z + -10)
3z + (-6 + 3z) = 7z + -3(z + -10)

Reorder the terms:
-6 + 3z + 3z = 7z + -3(z + -10)

Combine like terms: 3z + 3z = 6z
-6 + 6z = 7z + -3(z + -10)

Reorder the terms:
-6 + 6z = 7z + -3(-10 + z)
-6 + 6z = 7z + (-10 * -3 + z * -3)
-6 + 6z = 7z + (30 + -3z)

Reorder the terms:
-6 + 6z = 30 + 7z + -3z

Combine like terms: 7z + -3z = 4z
-6 + 6z = 30 + 4z

Solving
-6 + 6z = 30 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
-6 + 6z + -4z = 30 + 4z + -4z

Combine like terms: 6z + -4z = 2z
-6 + 2z = 30 + 4z + -4z

Combine like terms: 4z + -4z = 0
-6 + 2z = 30 + 0
-6 + 2z = 30

Add '6' to each side of the equation.
-6 + 6 + 2z = 30 + 6

Combine like terms: -6 + 6 = 0
0 + 2z = 30 + 6
2z = 30 + 6

Combine like terms: 30 + 6 = 36
2z = 36

Divide each side by '2'.
z = 18

Simplifying
z = 18