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

Solution for 9(z+3)-4(z-1)=2(z-3)+2(z-1) equation:

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

Reorder the terms:
9(3 + z) + -4(z + -1) = 2(z + -3) + 2(z + -1)
(3 * 9 + z * 9) + -4(z + -1) = 2(z + -3) + 2(z + -1)
(27 + 9z) + -4(z + -1) = 2(z + -3) + 2(z + -1)

Reorder the terms:
27 + 9z + -4(-1 + z) = 2(z + -3) + 2(z + -1)
27 + 9z + (-1 * -4 + z * -4) = 2(z + -3) + 2(z + -1)
27 + 9z + (4 + -4z) = 2(z + -3) + 2(z + -1)

Reorder the terms:
27 + 4 + 9z + -4z = 2(z + -3) + 2(z + -1)

Combine like terms: 27 + 4 = 31
31 + 9z + -4z = 2(z + -3) + 2(z + -1)

Combine like terms: 9z + -4z = 5z
31 + 5z = 2(z + -3) + 2(z + -1)

Reorder the terms:
31 + 5z = 2(-3 + z) + 2(z + -1)
31 + 5z = (-3 * 2 + z * 2) + 2(z + -1)
31 + 5z = (-6 + 2z) + 2(z + -1)

Reorder the terms:
31 + 5z = -6 + 2z + 2(-1 + z)
31 + 5z = -6 + 2z + (-1 * 2 + z * 2)
31 + 5z = -6 + 2z + (-2 + 2z)

Reorder the terms:
31 + 5z = -6 + -2 + 2z + 2z

Combine like terms: -6 + -2 = -8
31 + 5z = -8 + 2z + 2z

Combine like terms: 2z + 2z = 4z
31 + 5z = -8 + 4z

Solving
31 + 5z = -8 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
31 + 5z + -4z = -8 + 4z + -4z

Combine like terms: 5z + -4z = 1z
31 + 1z = -8 + 4z + -4z

Combine like terms: 4z + -4z = 0
31 + 1z = -8 + 0
31 + 1z = -8

Add '-31' to each side of the equation.
31 + -31 + 1z = -8 + -31

Combine like terms: 31 + -31 = 0
0 + 1z = -8 + -31
1z = -8 + -31

Combine like terms: -8 + -31 = -39
1z = -39

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

Simplifying
z = -39