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

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

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

Reorder the terms:
12(2 + z) + -4(z + -4) = 3(z + -1) + 4(z + -3)
(2 * 12 + z * 12) + -4(z + -4) = 3(z + -1) + 4(z + -3)
(24 + 12z) + -4(z + -4) = 3(z + -1) + 4(z + -3)

Reorder the terms:
24 + 12z + -4(-4 + z) = 3(z + -1) + 4(z + -3)
24 + 12z + (-4 * -4 + z * -4) = 3(z + -1) + 4(z + -3)
24 + 12z + (16 + -4z) = 3(z + -1) + 4(z + -3)

Reorder the terms:
24 + 16 + 12z + -4z = 3(z + -1) + 4(z + -3)

Combine like terms: 24 + 16 = 40
40 + 12z + -4z = 3(z + -1) + 4(z + -3)

Combine like terms: 12z + -4z = 8z
40 + 8z = 3(z + -1) + 4(z + -3)

Reorder the terms:
40 + 8z = 3(-1 + z) + 4(z + -3)
40 + 8z = (-1 * 3 + z * 3) + 4(z + -3)
40 + 8z = (-3 + 3z) + 4(z + -3)

Reorder the terms:
40 + 8z = -3 + 3z + 4(-3 + z)
40 + 8z = -3 + 3z + (-3 * 4 + z * 4)
40 + 8z = -3 + 3z + (-12 + 4z)

Reorder the terms:
40 + 8z = -3 + -12 + 3z + 4z

Combine like terms: -3 + -12 = -15
40 + 8z = -15 + 3z + 4z

Combine like terms: 3z + 4z = 7z
40 + 8z = -15 + 7z

Solving
40 + 8z = -15 + 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.
40 + 8z + -7z = -15 + 7z + -7z

Combine like terms: 8z + -7z = 1z
40 + 1z = -15 + 7z + -7z

Combine like terms: 7z + -7z = 0
40 + 1z = -15 + 0
40 + 1z = -15

Add '-40' to each side of the equation.
40 + -40 + 1z = -15 + -40

Combine like terms: 40 + -40 = 0
0 + 1z = -15 + -40
1z = -15 + -40

Combine like terms: -15 + -40 = -55
1z = -55

Divide each side by '1'.
z = -55

Simplifying
z = -55