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

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

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

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

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

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

Combine like terms: 9 + 4 = 13
13 + 9z + -4z = 2(z + -1) + 2(z + -3)

Combine like terms: 9z + -4z = 5z
13 + 5z = 2(z + -1) + 2(z + -3)

Reorder the terms:
13 + 5z = 2(-1 + z) + 2(z + -3)
13 + 5z = (-1 * 2 + z * 2) + 2(z + -3)
13 + 5z = (-2 + 2z) + 2(z + -3)

Reorder the terms:
13 + 5z = -2 + 2z + 2(-3 + z)
13 + 5z = -2 + 2z + (-3 * 2 + z * 2)
13 + 5z = -2 + 2z + (-6 + 2z)

Reorder the terms:
13 + 5z = -2 + -6 + 2z + 2z

Combine like terms: -2 + -6 = -8
13 + 5z = -8 + 2z + 2z

Combine like terms: 2z + 2z = 4z
13 + 5z = -8 + 4z

Solving
13 + 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.
13 + 5z + -4z = -8 + 4z + -4z

Combine like terms: 5z + -4z = 1z
13 + 1z = -8 + 4z + -4z

Combine like terms: 4z + -4z = 0
13 + 1z = -8 + 0
13 + 1z = -8

Add '-13' to each side of the equation.
13 + -13 + 1z = -8 + -13

Combine like terms: 13 + -13 = 0
0 + 1z = -8 + -13
1z = -8 + -13

Combine like terms: -8 + -13 = -21
1z = -21

Divide each side by '1'.
z = -21

Simplifying
z = -21