3(z-1)-4(5-z)=2(6+z)

Solution for 3(z-1)-4(5-z)=2(6+z) equation:

Simplifying
3(z + -1) + -4(5 + -1z) = 2(6 + z)

Reorder the terms:
3(-1 + z) + -4(5 + -1z) = 2(6 + z)
(-1 * 3 + z * 3) + -4(5 + -1z) = 2(6 + z)
(-3 + 3z) + -4(5 + -1z) = 2(6 + z)
-3 + 3z + (5 * -4 + -1z * -4) = 2(6 + z)
-3 + 3z + (-20 + 4z) = 2(6 + z)

Reorder the terms:
-3 + -20 + 3z + 4z = 2(6 + z)

Combine like terms: -3 + -20 = -23
-23 + 3z + 4z = 2(6 + z)

Combine like terms: 3z + 4z = 7z
-23 + 7z = 2(6 + z)
-23 + 7z = (6 * 2 + z * 2)
-23 + 7z = (12 + 2z)

Solving
-23 + 7z = 12 + 2z

Solving for variable 'z'.

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

Add '-2z' to each side of the equation.
-23 + 7z + -2z = 12 + 2z + -2z

Combine like terms: 7z + -2z = 5z
-23 + 5z = 12 + 2z + -2z

Combine like terms: 2z + -2z = 0
-23 + 5z = 12 + 0
-23 + 5z = 12

Add '23' to each side of the equation.
-23 + 23 + 5z = 12 + 23

Combine like terms: -23 + 23 = 0
0 + 5z = 12 + 23
5z = 12 + 23

Combine like terms: 12 + 23 = 35
5z = 35

Divide each side by '5'.
z = 7

Simplifying
z = 7