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

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

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

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

Reorder the terms:
9 + 9z + -3(-4 + z) = 2(z + -4) + 3(z + -4)
9 + 9z + (-4 * -3 + z * -3) = 2(z + -4) + 3(z + -4)
9 + 9z + (12 + -3z) = 2(z + -4) + 3(z + -4)

Reorder the terms:
9 + 12 + 9z + -3z = 2(z + -4) + 3(z + -4)

Combine like terms: 9 + 12 = 21
21 + 9z + -3z = 2(z + -4) + 3(z + -4)

Combine like terms: 9z + -3z = 6z
21 + 6z = 2(z + -4) + 3(z + -4)

Reorder the terms:
21 + 6z = 2(-4 + z) + 3(z + -4)
21 + 6z = (-4 * 2 + z * 2) + 3(z + -4)
21 + 6z = (-8 + 2z) + 3(z + -4)

Reorder the terms:
21 + 6z = -8 + 2z + 3(-4 + z)
21 + 6z = -8 + 2z + (-4 * 3 + z * 3)
21 + 6z = -8 + 2z + (-12 + 3z)

Reorder the terms:
21 + 6z = -8 + -12 + 2z + 3z

Combine like terms: -8 + -12 = -20
21 + 6z = -20 + 2z + 3z

Combine like terms: 2z + 3z = 5z
21 + 6z = -20 + 5z

Solving
21 + 6z = -20 + 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.
21 + 6z + -5z = -20 + 5z + -5z

Combine like terms: 6z + -5z = 1z
21 + 1z = -20 + 5z + -5z

Combine like terms: 5z + -5z = 0
21 + 1z = -20 + 0
21 + 1z = -20

Add '-21' to each side of the equation.
21 + -21 + 1z = -20 + -21

Combine like terms: 21 + -21 = 0
0 + 1z = -20 + -21
1z = -20 + -21

Combine like terms: -20 + -21 = -41
1z = -41

Divide each side by '1'.
z = -41

Simplifying
z = -41