9(z+3)-3(z-2)=3(z-3)+2(z-2)

Solution for 9(z+3)-3(z-2)=3(z-3)+2(z-2) equation:

Simplifying
9(z + 3) + -3(z + -2) = 3(z + -3) + 2(z + -2)

Reorder the terms:
9(3 + z) + -3(z + -2) = 3(z + -3) + 2(z + -2)
(3 * 9 + z * 9) + -3(z + -2) = 3(z + -3) + 2(z + -2)
(27 + 9z) + -3(z + -2) = 3(z + -3) + 2(z + -2)

Reorder the terms:
27 + 9z + -3(-2 + z) = 3(z + -3) + 2(z + -2)
27 + 9z + (-2 * -3 + z * -3) = 3(z + -3) + 2(z + -2)
27 + 9z + (6 + -3z) = 3(z + -3) + 2(z + -2)

Reorder the terms:
27 + 6 + 9z + -3z = 3(z + -3) + 2(z + -2)

Combine like terms: 27 + 6 = 33
33 + 9z + -3z = 3(z + -3) + 2(z + -2)

Combine like terms: 9z + -3z = 6z
33 + 6z = 3(z + -3) + 2(z + -2)

Reorder the terms:
33 + 6z = 3(-3 + z) + 2(z + -2)
33 + 6z = (-3 * 3 + z * 3) + 2(z + -2)
33 + 6z = (-9 + 3z) + 2(z + -2)

Reorder the terms:
33 + 6z = -9 + 3z + 2(-2 + z)
33 + 6z = -9 + 3z + (-2 * 2 + z * 2)
33 + 6z = -9 + 3z + (-4 + 2z)

Reorder the terms:
33 + 6z = -9 + -4 + 3z + 2z

Combine like terms: -9 + -4 = -13
33 + 6z = -13 + 3z + 2z

Combine like terms: 3z + 2z = 5z
33 + 6z = -13 + 5z

Solving
33 + 6z = -13 + 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.
33 + 6z + -5z = -13 + 5z + -5z

Combine like terms: 6z + -5z = 1z
33 + 1z = -13 + 5z + -5z

Combine like terms: 5z + -5z = 0
33 + 1z = -13 + 0
33 + 1z = -13

Add '-33' to each side of the equation.
33 + -33 + 1z = -13 + -33

Combine like terms: 33 + -33 = 0
0 + 1z = -13 + -33
1z = -13 + -33

Combine like terms: -13 + -33 = -46
1z = -46

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

Simplifying
z = -46