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

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

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

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

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

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

Combine like terms: 12 + 8 = 20
20 + 12z + -4z = 4(z + -2) + 3(z + -2)

Combine like terms: 12z + -4z = 8z
20 + 8z = 4(z + -2) + 3(z + -2)

Reorder the terms:
20 + 8z = 4(-2 + z) + 3(z + -2)
20 + 8z = (-2 * 4 + z * 4) + 3(z + -2)
20 + 8z = (-8 + 4z) + 3(z + -2)

Reorder the terms:
20 + 8z = -8 + 4z + 3(-2 + z)
20 + 8z = -8 + 4z + (-2 * 3 + z * 3)
20 + 8z = -8 + 4z + (-6 + 3z)

Reorder the terms:
20 + 8z = -8 + -6 + 4z + 3z

Combine like terms: -8 + -6 = -14
20 + 8z = -14 + 4z + 3z

Combine like terms: 4z + 3z = 7z
20 + 8z = -14 + 7z

Solving
20 + 8z = -14 + 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 = -14 + 7z + -7z

Combine like terms: 8z + -7z = 1z
20 + 1z = -14 + 7z + -7z

Combine like terms: 7z + -7z = 0
20 + 1z = -14 + 0
20 + 1z = -14

Add '-20' to each side of the equation.
20 + -20 + 1z = -14 + -20

Combine like terms: 20 + -20 = 0
0 + 1z = -14 + -20
1z = -14 + -20

Combine like terms: -14 + -20 = -34
1z = -34

Divide each side by '1'.
z = -34

Simplifying
z = -34