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

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

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

Reorder the terms:
8(3 + z) + -2(z + -4) = 3(z + -3) + 2(z + -1)
(3 * 8 + z * 8) + -2(z + -4) = 3(z + -3) + 2(z + -1)
(24 + 8z) + -2(z + -4) = 3(z + -3) + 2(z + -1)

Reorder the terms:
24 + 8z + -2(-4 + z) = 3(z + -3) + 2(z + -1)
24 + 8z + (-4 * -2 + z * -2) = 3(z + -3) + 2(z + -1)
24 + 8z + (8 + -2z) = 3(z + -3) + 2(z + -1)

Reorder the terms:
24 + 8 + 8z + -2z = 3(z + -3) + 2(z + -1)

Combine like terms: 24 + 8 = 32
32 + 8z + -2z = 3(z + -3) + 2(z + -1)

Combine like terms: 8z + -2z = 6z
32 + 6z = 3(z + -3) + 2(z + -1)

Reorder the terms:
32 + 6z = 3(-3 + z) + 2(z + -1)
32 + 6z = (-3 * 3 + z * 3) + 2(z + -1)
32 + 6z = (-9 + 3z) + 2(z + -1)

Reorder the terms:
32 + 6z = -9 + 3z + 2(-1 + z)
32 + 6z = -9 + 3z + (-1 * 2 + z * 2)
32 + 6z = -9 + 3z + (-2 + 2z)

Reorder the terms:
32 + 6z = -9 + -2 + 3z + 2z

Combine like terms: -9 + -2 = -11
32 + 6z = -11 + 3z + 2z

Combine like terms: 3z + 2z = 5z
32 + 6z = -11 + 5z

Solving
32 + 6z = -11 + 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.
32 + 6z + -5z = -11 + 5z + -5z

Combine like terms: 6z + -5z = 1z
32 + 1z = -11 + 5z + -5z

Combine like terms: 5z + -5z = 0
32 + 1z = -11 + 0
32 + 1z = -11

Add '-32' to each side of the equation.
32 + -32 + 1z = -11 + -32

Combine like terms: 32 + -32 = 0
0 + 1z = -11 + -32
1z = -11 + -32

Combine like terms: -11 + -32 = -43
1z = -43

Divide each side by '1'.
z = -43

Simplifying
z = -43