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

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

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

Reorder the terms:
8(4 + z) + -2(z + -3) = 2(z + -1) + 3(z + -2)
(4 * 8 + z * 8) + -2(z + -3) = 2(z + -1) + 3(z + -2)
(32 + 8z) + -2(z + -3) = 2(z + -1) + 3(z + -2)

Reorder the terms:
32 + 8z + -2(-3 + z) = 2(z + -1) + 3(z + -2)
32 + 8z + (-3 * -2 + z * -2) = 2(z + -1) + 3(z + -2)
32 + 8z + (6 + -2z) = 2(z + -1) + 3(z + -2)

Reorder the terms:
32 + 6 + 8z + -2z = 2(z + -1) + 3(z + -2)

Combine like terms: 32 + 6 = 38
38 + 8z + -2z = 2(z + -1) + 3(z + -2)

Combine like terms: 8z + -2z = 6z
38 + 6z = 2(z + -1) + 3(z + -2)

Reorder the terms:
38 + 6z = 2(-1 + z) + 3(z + -2)
38 + 6z = (-1 * 2 + z * 2) + 3(z + -2)
38 + 6z = (-2 + 2z) + 3(z + -2)

Reorder the terms:
38 + 6z = -2 + 2z + 3(-2 + z)
38 + 6z = -2 + 2z + (-2 * 3 + z * 3)
38 + 6z = -2 + 2z + (-6 + 3z)

Reorder the terms:
38 + 6z = -2 + -6 + 2z + 3z

Combine like terms: -2 + -6 = -8
38 + 6z = -8 + 2z + 3z

Combine like terms: 2z + 3z = 5z
38 + 6z = -8 + 5z

Solving
38 + 6z = -8 + 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.
38 + 6z + -5z = -8 + 5z + -5z

Combine like terms: 6z + -5z = 1z
38 + 1z = -8 + 5z + -5z

Combine like terms: 5z + -5z = 0
38 + 1z = -8 + 0
38 + 1z = -8

Add '-38' to each side of the equation.
38 + -38 + 1z = -8 + -38

Combine like terms: 38 + -38 = 0
0 + 1z = -8 + -38
1z = -8 + -38

Combine like terms: -8 + -38 = -46
1z = -46

Divide each side by '1'.
z = -46

Simplifying
z = -46