9(z+1)-3(z-1)=3(z-3)+2(z-3)

Solution for 9(z+1)-3(z-1)=3(z-3)+2(z-3) equation:

Simplifying
9(z + 1) + -3(z + -1) = 3(z + -3) + 2(z + -3)

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

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

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

Combine like terms: 9 + 3 = 12
12 + 9z + -3z = 3(z + -3) + 2(z + -3)

Combine like terms: 9z + -3z = 6z
12 + 6z = 3(z + -3) + 2(z + -3)

Reorder the terms:
12 + 6z = 3(-3 + z) + 2(z + -3)
12 + 6z = (-3 * 3 + z * 3) + 2(z + -3)
12 + 6z = (-9 + 3z) + 2(z + -3)

Reorder the terms:
12 + 6z = -9 + 3z + 2(-3 + z)
12 + 6z = -9 + 3z + (-3 * 2 + z * 2)
12 + 6z = -9 + 3z + (-6 + 2z)

Reorder the terms:
12 + 6z = -9 + -6 + 3z + 2z

Combine like terms: -9 + -6 = -15
12 + 6z = -15 + 3z + 2z

Combine like terms: 3z + 2z = 5z
12 + 6z = -15 + 5z

Solving
12 + 6z = -15 + 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.
12 + 6z + -5z = -15 + 5z + -5z

Combine like terms: 6z + -5z = 1z
12 + 1z = -15 + 5z + -5z

Combine like terms: 5z + -5z = 0
12 + 1z = -15 + 0
12 + 1z = -15

Add '-12' to each side of the equation.
12 + -12 + 1z = -15 + -12

Combine like terms: 12 + -12 = 0
0 + 1z = -15 + -12
1z = -15 + -12

Combine like terms: -15 + -12 = -27
1z = -27

Divide each side by '1'.
z = -27

Simplifying
z = -27