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

Solution for 8(z-1)-2(z-2)=3(z-4)+2(z-4) equation:

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

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

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

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

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

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

Reorder the terms:
-4 + 6z = 3(-4 + z) + 2(z + -4)
-4 + 6z = (-4 * 3 + z * 3) + 2(z + -4)
-4 + 6z = (-12 + 3z) + 2(z + -4)

Reorder the terms:
-4 + 6z = -12 + 3z + 2(-4 + z)
-4 + 6z = -12 + 3z + (-4 * 2 + z * 2)
-4 + 6z = -12 + 3z + (-8 + 2z)

Reorder the terms:
-4 + 6z = -12 + -8 + 3z + 2z

Combine like terms: -12 + -8 = -20
-4 + 6z = -20 + 3z + 2z

Combine like terms: 3z + 2z = 5z
-4 + 6z = -20 + 5z

Solving
-4 + 6z = -20 + 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.
-4 + 6z + -5z = -20 + 5z + -5z

Combine like terms: 6z + -5z = 1z
-4 + 1z = -20 + 5z + -5z

Combine like terms: 5z + -5z = 0
-4 + 1z = -20 + 0
-4 + 1z = -20

Add '4' to each side of the equation.
-4 + 4 + 1z = -20 + 4

Combine like terms: -4 + 4 = 0
0 + 1z = -20 + 4
1z = -20 + 4

Combine like terms: -20 + 4 = -16
1z = -16

Divide each side by '1'.
z = -16

Simplifying
z = -16