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

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

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

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

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

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

Combine like terms: 9 + 6 = 15
15 + 9z + -2z = 3(z + -3) + 3(z + -1)

Combine like terms: 9z + -2z = 7z
15 + 7z = 3(z + -3) + 3(z + -1)

Reorder the terms:
15 + 7z = 3(-3 + z) + 3(z + -1)
15 + 7z = (-3 * 3 + z * 3) + 3(z + -1)
15 + 7z = (-9 + 3z) + 3(z + -1)

Reorder the terms:
15 + 7z = -9 + 3z + 3(-1 + z)
15 + 7z = -9 + 3z + (-1 * 3 + z * 3)
15 + 7z = -9 + 3z + (-3 + 3z)

Reorder the terms:
15 + 7z = -9 + -3 + 3z + 3z

Combine like terms: -9 + -3 = -12
15 + 7z = -12 + 3z + 3z

Combine like terms: 3z + 3z = 6z
15 + 7z = -12 + 6z

Solving
15 + 7z = -12 + 6z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-6z' to each side of the equation.
15 + 7z + -6z = -12 + 6z + -6z

Combine like terms: 7z + -6z = 1z
15 + 1z = -12 + 6z + -6z

Combine like terms: 6z + -6z = 0
15 + 1z = -12 + 0
15 + 1z = -12

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

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

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

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

Simplifying
z = -27