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

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

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

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

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

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

Combine like terms: 36 + 12 = 48
48 + 12z + -4z = 4(z + -1) + 3(z + -4)

Combine like terms: 12z + -4z = 8z
48 + 8z = 4(z + -1) + 3(z + -4)

Reorder the terms:
48 + 8z = 4(-1 + z) + 3(z + -4)
48 + 8z = (-1 * 4 + z * 4) + 3(z + -4)
48 + 8z = (-4 + 4z) + 3(z + -4)

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

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

Combine like terms: -4 + -12 = -16
48 + 8z = -16 + 4z + 3z

Combine like terms: 4z + 3z = 7z
48 + 8z = -16 + 7z

Solving
48 + 8z = -16 + 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.
48 + 8z + -7z = -16 + 7z + -7z

Combine like terms: 8z + -7z = 1z
48 + 1z = -16 + 7z + -7z

Combine like terms: 7z + -7z = 0
48 + 1z = -16 + 0
48 + 1z = -16

Add '-48' to each side of the equation.
48 + -48 + 1z = -16 + -48

Combine like terms: 48 + -48 = 0
0 + 1z = -16 + -48
1z = -16 + -48

Combine like terms: -16 + -48 = -64
1z = -64

Divide each side by '1'.
z = -64

Simplifying
z = -64