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

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

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

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

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

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

Combine like terms: 48 + 4 = 52
52 + 12z + -4z = 3(z + -3) + 4(z + -1)

Combine like terms: 12z + -4z = 8z
52 + 8z = 3(z + -3) + 4(z + -1)

Reorder the terms:
52 + 8z = 3(-3 + z) + 4(z + -1)
52 + 8z = (-3 * 3 + z * 3) + 4(z + -1)
52 + 8z = (-9 + 3z) + 4(z + -1)

Reorder the terms:
52 + 8z = -9 + 3z + 4(-1 + z)
52 + 8z = -9 + 3z + (-1 * 4 + z * 4)
52 + 8z = -9 + 3z + (-4 + 4z)

Reorder the terms:
52 + 8z = -9 + -4 + 3z + 4z

Combine like terms: -9 + -4 = -13
52 + 8z = -13 + 3z + 4z

Combine like terms: 3z + 4z = 7z
52 + 8z = -13 + 7z

Solving
52 + 8z = -13 + 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 = -13 + 7z + -7z

Combine like terms: 8z + -7z = 1z
52 + 1z = -13 + 7z + -7z

Combine like terms: 7z + -7z = 0
52 + 1z = -13 + 0
52 + 1z = -13

Add '-52' to each side of the equation.
52 + -52 + 1z = -13 + -52

Combine like terms: 52 + -52 = 0
0 + 1z = -13 + -52
1z = -13 + -52

Combine like terms: -13 + -52 = -65
1z = -65

Divide each side by '1'.
z = -65

Simplifying
z = -65