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

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

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

Reorder the terms:
12(4 + z) + -4(z + -2) = 4(z + -4) + 3(z + -4)
(4 * 12 + z * 12) + -4(z + -2) = 4(z + -4) + 3(z + -4)
(48 + 12z) + -4(z + -2) = 4(z + -4) + 3(z + -4)

Reorder the terms:
48 + 12z + -4(-2 + z) = 4(z + -4) + 3(z + -4)
48 + 12z + (-2 * -4 + z * -4) = 4(z + -4) + 3(z + -4)
48 + 12z + (8 + -4z) = 4(z + -4) + 3(z + -4)

Reorder the terms:
48 + 8 + 12z + -4z = 4(z + -4) + 3(z + -4)

Combine like terms: 48 + 8 = 56
56 + 12z + -4z = 4(z + -4) + 3(z + -4)

Combine like terms: 12z + -4z = 8z
56 + 8z = 4(z + -4) + 3(z + -4)

Reorder the terms:
56 + 8z = 4(-4 + z) + 3(z + -4)
56 + 8z = (-4 * 4 + z * 4) + 3(z + -4)
56 + 8z = (-16 + 4z) + 3(z + -4)

Reorder the terms:
56 + 8z = -16 + 4z + 3(-4 + z)
56 + 8z = -16 + 4z + (-4 * 3 + z * 3)
56 + 8z = -16 + 4z + (-12 + 3z)

Reorder the terms:
56 + 8z = -16 + -12 + 4z + 3z

Combine like terms: -16 + -12 = -28
56 + 8z = -28 + 4z + 3z

Combine like terms: 4z + 3z = 7z
56 + 8z = -28 + 7z

Solving
56 + 8z = -28 + 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.
56 + 8z + -7z = -28 + 7z + -7z

Combine like terms: 8z + -7z = 1z
56 + 1z = -28 + 7z + -7z

Combine like terms: 7z + -7z = 0
56 + 1z = -28 + 0
56 + 1z = -28

Add '-56' to each side of the equation.
56 + -56 + 1z = -28 + -56

Combine like terms: 56 + -56 = 0
0 + 1z = -28 + -56
1z = -28 + -56

Combine like terms: -28 + -56 = -84
1z = -84

Divide each side by '1'.
z = -84

Simplifying
z = -84