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

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

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

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

Reorder the terms:
9 + 9z + -2(-4 + z) = 4(z + -1) + 2(z + -3)
9 + 9z + (-4 * -2 + z * -2) = 4(z + -1) + 2(z + -3)
9 + 9z + (8 + -2z) = 4(z + -1) + 2(z + -3)

Reorder the terms:
9 + 8 + 9z + -2z = 4(z + -1) + 2(z + -3)

Combine like terms: 9 + 8 = 17
17 + 9z + -2z = 4(z + -1) + 2(z + -3)

Combine like terms: 9z + -2z = 7z
17 + 7z = 4(z + -1) + 2(z + -3)

Reorder the terms:
17 + 7z = 4(-1 + z) + 2(z + -3)
17 + 7z = (-1 * 4 + z * 4) + 2(z + -3)
17 + 7z = (-4 + 4z) + 2(z + -3)

Reorder the terms:
17 + 7z = -4 + 4z + 2(-3 + z)
17 + 7z = -4 + 4z + (-3 * 2 + z * 2)
17 + 7z = -4 + 4z + (-6 + 2z)

Reorder the terms:
17 + 7z = -4 + -6 + 4z + 2z

Combine like terms: -4 + -6 = -10
17 + 7z = -10 + 4z + 2z

Combine like terms: 4z + 2z = 6z
17 + 7z = -10 + 6z

Solving
17 + 7z = -10 + 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.
17 + 7z + -6z = -10 + 6z + -6z

Combine like terms: 7z + -6z = 1z
17 + 1z = -10 + 6z + -6z

Combine like terms: 6z + -6z = 0
17 + 1z = -10 + 0
17 + 1z = -10

Add '-17' to each side of the equation.
17 + -17 + 1z = -10 + -17

Combine like terms: 17 + -17 = 0
0 + 1z = -10 + -17
1z = -10 + -17

Combine like terms: -10 + -17 = -27
1z = -27

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

Simplifying
z = -27