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

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

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

Reorder the terms:
12(4 + z) + -4(z + -1) = 4(z + -3) + 3(z + -4)
(4 * 12 + z * 12) + -4(z + -1) = 4(z + -3) + 3(z + -4)
(48 + 12z) + -4(z + -1) = 4(z + -3) + 3(z + -4)

Reorder the terms:
48 + 12z + -4(-1 + z) = 4(z + -3) + 3(z + -4)
48 + 12z + (-1 * -4 + z * -4) = 4(z + -3) + 3(z + -4)
48 + 12z + (4 + -4z) = 4(z + -3) + 3(z + -4)

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

Combine like terms: 48 + 4 = 52
52 + 12z + -4z = 4(z + -3) + 3(z + -4)

Combine like terms: 12z + -4z = 8z
52 + 8z = 4(z + -3) + 3(z + -4)

Reorder the terms:
52 + 8z = 4(-3 + z) + 3(z + -4)
52 + 8z = (-3 * 4 + z * 4) + 3(z + -4)
52 + 8z = (-12 + 4z) + 3(z + -4)

Reorder the terms:
52 + 8z = -12 + 4z + 3(-4 + z)
52 + 8z = -12 + 4z + (-4 * 3 + z * 3)
52 + 8z = -12 + 4z + (-12 + 3z)

Reorder the terms:
52 + 8z = -12 + -12 + 4z + 3z

Combine like terms: -12 + -12 = -24
52 + 8z = -24 + 4z + 3z

Combine like terms: 4z + 3z = 7z
52 + 8z = -24 + 7z

Solving
52 + 8z = -24 + 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.
52 + 8z + -7z = -24 + 7z + -7z

Combine like terms: 8z + -7z = 1z
52 + 1z = -24 + 7z + -7z

Combine like terms: 7z + -7z = 0
52 + 1z = -24 + 0
52 + 1z = -24

Add '-52' to each side of the equation.
52 + -52 + 1z = -24 + -52

Combine like terms: 52 + -52 = 0
0 + 1z = -24 + -52
1z = -24 + -52

Combine like terms: -24 + -52 = -76
1z = -76

Divide each side by '1'.
z = -76

Simplifying
z = -76