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

Solution for 12(z+3)-3(z-2)=4(z-2)+4(z-1) equation:

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

Reorder the terms:
12(3 + z) + -3(z + -2) = 4(z + -2) + 4(z + -1)
(3 * 12 + z * 12) + -3(z + -2) = 4(z + -2) + 4(z + -1)
(36 + 12z) + -3(z + -2) = 4(z + -2) + 4(z + -1)

Reorder the terms:
36 + 12z + -3(-2 + z) = 4(z + -2) + 4(z + -1)
36 + 12z + (-2 * -3 + z * -3) = 4(z + -2) + 4(z + -1)
36 + 12z + (6 + -3z) = 4(z + -2) + 4(z + -1)

Reorder the terms:
36 + 6 + 12z + -3z = 4(z + -2) + 4(z + -1)

Combine like terms: 36 + 6 = 42
42 + 12z + -3z = 4(z + -2) + 4(z + -1)

Combine like terms: 12z + -3z = 9z
42 + 9z = 4(z + -2) + 4(z + -1)

Reorder the terms:
42 + 9z = 4(-2 + z) + 4(z + -1)
42 + 9z = (-2 * 4 + z * 4) + 4(z + -1)
42 + 9z = (-8 + 4z) + 4(z + -1)

Reorder the terms:
42 + 9z = -8 + 4z + 4(-1 + z)
42 + 9z = -8 + 4z + (-1 * 4 + z * 4)
42 + 9z = -8 + 4z + (-4 + 4z)

Reorder the terms:
42 + 9z = -8 + -4 + 4z + 4z

Combine like terms: -8 + -4 = -12
42 + 9z = -12 + 4z + 4z

Combine like terms: 4z + 4z = 8z
42 + 9z = -12 + 8z

Solving
42 + 9z = -12 + 8z

Solving for variable 'z'.

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

Add '-8z' to each side of the equation.
42 + 9z + -8z = -12 + 8z + -8z

Combine like terms: 9z + -8z = 1z
42 + 1z = -12 + 8z + -8z

Combine like terms: 8z + -8z = 0
42 + 1z = -12 + 0
42 + 1z = -12

Add '-42' to each side of the equation.
42 + -42 + 1z = -12 + -42

Combine like terms: 42 + -42 = 0
0 + 1z = -12 + -42
1z = -12 + -42

Combine like terms: -12 + -42 = -54
1z = -54

Divide each side by '1'.
z = -54

Simplifying
z = -54