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

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

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

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

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

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

Combine like terms: 12 + 8 = 20
20 + 12z + -4z = 3(z + -3) + 4(z + -3)

Combine like terms: 12z + -4z = 8z
20 + 8z = 3(z + -3) + 4(z + -3)

Reorder the terms:
20 + 8z = 3(-3 + z) + 4(z + -3)
20 + 8z = (-3 * 3 + z * 3) + 4(z + -3)
20 + 8z = (-9 + 3z) + 4(z + -3)

Reorder the terms:
20 + 8z = -9 + 3z + 4(-3 + z)
20 + 8z = -9 + 3z + (-3 * 4 + z * 4)
20 + 8z = -9 + 3z + (-12 + 4z)

Reorder the terms:
20 + 8z = -9 + -12 + 3z + 4z

Combine like terms: -9 + -12 = -21
20 + 8z = -21 + 3z + 4z

Combine like terms: 3z + 4z = 7z
20 + 8z = -21 + 7z

Solving
20 + 8z = -21 + 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.
20 + 8z + -7z = -21 + 7z + -7z

Combine like terms: 8z + -7z = 1z
20 + 1z = -21 + 7z + -7z

Combine like terms: 7z + -7z = 0
20 + 1z = -21 + 0
20 + 1z = -21

Add '-20' to each side of the equation.
20 + -20 + 1z = -21 + -20

Combine like terms: 20 + -20 = 0
0 + 1z = -21 + -20
1z = -21 + -20

Combine like terms: -21 + -20 = -41
1z = -41

Divide each side by '1'.
z = -41

Simplifying
z = -41