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

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


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

Reorder the terms:
12(3 + z) + -4(z + -2) = 4(z + -2) + 3(z + -1)
(3 * 12 + z * 12) + -4(z + -2) = 4(z + -2) + 3(z + -1)
(36 + 12z) + -4(z + -2) = 4(z + -2) + 3(z + -1)

Reorder the terms:
36 + 12z + -4(-2 + z) = 4(z + -2) + 3(z + -1)
36 + 12z + (-2 * -4 + z * -4) = 4(z + -2) + 3(z + -1)
36 + 12z + (8 + -4z) = 4(z + -2) + 3(z + -1)

Reorder the terms:
36 + 8 + 12z + -4z = 4(z + -2) + 3(z + -1)

Combine like terms: 36 + 8 = 44
44 + 12z + -4z = 4(z + -2) + 3(z + -1)

Combine like terms: 12z + -4z = 8z
44 + 8z = 4(z + -2) + 3(z + -1)

Reorder the terms:
44 + 8z = 4(-2 + z) + 3(z + -1)
44 + 8z = (-2 * 4 + z * 4) + 3(z + -1)
44 + 8z = (-8 + 4z) + 3(z + -1)

Reorder the terms:
44 + 8z = -8 + 4z + 3(-1 + z)
44 + 8z = -8 + 4z + (-1 * 3 + z * 3)
44 + 8z = -8 + 4z + (-3 + 3z)

Reorder the terms:
44 + 8z = -8 + -3 + 4z + 3z

Combine like terms: -8 + -3 = -11
44 + 8z = -11 + 4z + 3z

Combine like terms: 4z + 3z = 7z
44 + 8z = -11 + 7z

Solving
44 + 8z = -11 + 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.
44 + 8z + -7z = -11 + 7z + -7z

Combine like terms: 8z + -7z = 1z
44 + 1z = -11 + 7z + -7z

Combine like terms: 7z + -7z = 0
44 + 1z = -11 + 0
44 + 1z = -11

Add '-44' to each side of the equation.
44 + -44 + 1z = -11 + -44

Combine like terms: 44 + -44 = 0
0 + 1z = -11 + -44
1z = -11 + -44

Combine like terms: -11 + -44 = -55
1z = -55

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

Simplifying
z = -55

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