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

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

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

Reorder the terms:
8(2 + z) + -2(z + -3) = 2(z + -4) + 3(z + -3)
(2 * 8 + z * 8) + -2(z + -3) = 2(z + -4) + 3(z + -3)
(16 + 8z) + -2(z + -3) = 2(z + -4) + 3(z + -3)

Reorder the terms:
16 + 8z + -2(-3 + z) = 2(z + -4) + 3(z + -3)
16 + 8z + (-3 * -2 + z * -2) = 2(z + -4) + 3(z + -3)
16 + 8z + (6 + -2z) = 2(z + -4) + 3(z + -3)

Reorder the terms:
16 + 6 + 8z + -2z = 2(z + -4) + 3(z + -3)

Combine like terms: 16 + 6 = 22
22 + 8z + -2z = 2(z + -4) + 3(z + -3)

Combine like terms: 8z + -2z = 6z
22 + 6z = 2(z + -4) + 3(z + -3)

Reorder the terms:
22 + 6z = 2(-4 + z) + 3(z + -3)
22 + 6z = (-4 * 2 + z * 2) + 3(z + -3)
22 + 6z = (-8 + 2z) + 3(z + -3)

Reorder the terms:
22 + 6z = -8 + 2z + 3(-3 + z)
22 + 6z = -8 + 2z + (-3 * 3 + z * 3)
22 + 6z = -8 + 2z + (-9 + 3z)

Reorder the terms:
22 + 6z = -8 + -9 + 2z + 3z

Combine like terms: -8 + -9 = -17
22 + 6z = -17 + 2z + 3z

Combine like terms: 2z + 3z = 5z
22 + 6z = -17 + 5z

Solving
22 + 6z = -17 + 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.
22 + 6z + -5z = -17 + 5z + -5z

Combine like terms: 6z + -5z = 1z
22 + 1z = -17 + 5z + -5z

Combine like terms: 5z + -5z = 0
22 + 1z = -17 + 0
22 + 1z = -17

Add '-22' to each side of the equation.
22 + -22 + 1z = -17 + -22

Combine like terms: 22 + -22 = 0
0 + 1z = -17 + -22
1z = -17 + -22

Combine like terms: -17 + -22 = -39
1z = -39

Divide each side by '1'.
z = -39

Simplifying
z = -39