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

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

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

Reorder the terms:
-2(-4 + z) + -1(3z + -1z) = 3(z + -1) + 2(z + -3)
(-4 * -2 + z * -2) + -1(3z + -1z) = 3(z + -1) + 2(z + -3)
(8 + -2z) + -1(3z + -1z) = 3(z + -1) + 2(z + -3)

Combine like terms: 3z + -1z = 2z
8 + -2z + -1(2z) = 3(z + -1) + 2(z + -3)

Remove parenthesis around (2z)
8 + -2z + -1 * 2z = 3(z + -1) + 2(z + -3)

Multiply -1 * 2
8 + -2z + -2z = 3(z + -1) + 2(z + -3)

Combine like terms: -2z + -2z = -4z
8 + -4z = 3(z + -1) + 2(z + -3)

Reorder the terms:
8 + -4z = 3(-1 + z) + 2(z + -3)
8 + -4z = (-1 * 3 + z * 3) + 2(z + -3)
8 + -4z = (-3 + 3z) + 2(z + -3)

Reorder the terms:
8 + -4z = -3 + 3z + 2(-3 + z)
8 + -4z = -3 + 3z + (-3 * 2 + z * 2)
8 + -4z = -3 + 3z + (-6 + 2z)

Reorder the terms:
8 + -4z = -3 + -6 + 3z + 2z

Combine like terms: -3 + -6 = -9
8 + -4z = -9 + 3z + 2z

Combine like terms: 3z + 2z = 5z
8 + -4z = -9 + 5z

Solving
8 + -4z = -9 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
8 + -4z + -5z = -9 + 5z + -5z

Combine like terms: -4z + -5z = -9z
8 + -9z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
8 + -9z = -9 + 0
8 + -9z = -9

Add '-8' to each side of the equation.
8 + -8 + -9z = -9 + -8

Combine like terms: 8 + -8 = 0
0 + -9z = -9 + -8
-9z = -9 + -8

Combine like terms: -9 + -8 = -17
-9z = -17

Divide each side by '-9'.
z = 1.888888889

Simplifying
z = 1.888888889