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

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

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

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

Reorder the terms:
12 + 12z + -4(-4 + z) = 3(z + -2) + 4(z + -2)
12 + 12z + (-4 * -4 + z * -4) = 3(z + -2) + 4(z + -2)
12 + 12z + (16 + -4z) = 3(z + -2) + 4(z + -2)

Reorder the terms:
12 + 16 + 12z + -4z = 3(z + -2) + 4(z + -2)

Combine like terms: 12 + 16 = 28
28 + 12z + -4z = 3(z + -2) + 4(z + -2)

Combine like terms: 12z + -4z = 8z
28 + 8z = 3(z + -2) + 4(z + -2)

Reorder the terms:
28 + 8z = 3(-2 + z) + 4(z + -2)
28 + 8z = (-2 * 3 + z * 3) + 4(z + -2)
28 + 8z = (-6 + 3z) + 4(z + -2)

Reorder the terms:
28 + 8z = -6 + 3z + 4(-2 + z)
28 + 8z = -6 + 3z + (-2 * 4 + z * 4)
28 + 8z = -6 + 3z + (-8 + 4z)

Reorder the terms:
28 + 8z = -6 + -8 + 3z + 4z

Combine like terms: -6 + -8 = -14
28 + 8z = -14 + 3z + 4z

Combine like terms: 3z + 4z = 7z
28 + 8z = -14 + 7z

Solving
28 + 8z = -14 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
28 + 8z + -7z = -14 + 7z + -7z

Combine like terms: 8z + -7z = 1z
28 + 1z = -14 + 7z + -7z

Combine like terms: 7z + -7z = 0
28 + 1z = -14 + 0
28 + 1z = -14

Add '-28' to each side of the equation.
28 + -28 + 1z = -14 + -28

Combine like terms: 28 + -28 = 0
0 + 1z = -14 + -28
1z = -14 + -28

Combine like terms: -14 + -28 = -42
1z = -42

Divide each side by '1'.
z = -42

Simplifying
z = -42