# 3(4Z-1)-4(Z+8)=3(Z+1)

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## Solution for 3(4Z-1)-4(Z+8)=3(Z+1) equation:

Simplifying
3(4Z + -1) + -4(Z + 8) = 3(Z + 1)

Reorder the terms:
3(-1 + 4Z) + -4(Z + 8) = 3(Z + 1)
(-1 * 3 + 4Z * 3) + -4(Z + 8) = 3(Z + 1)
(-3 + 12Z) + -4(Z + 8) = 3(Z + 1)

Reorder the terms:
-3 + 12Z + -4(8 + Z) = 3(Z + 1)
-3 + 12Z + (8 * -4 + Z * -4) = 3(Z + 1)
-3 + 12Z + (-32 + -4Z) = 3(Z + 1)

Reorder the terms:
-3 + -32 + 12Z + -4Z = 3(Z + 1)

Combine like terms: -3 + -32 = -35
-35 + 12Z + -4Z = 3(Z + 1)

Combine like terms: 12Z + -4Z = 8Z
-35 + 8Z = 3(Z + 1)

Reorder the terms:
-35 + 8Z = 3(1 + Z)
-35 + 8Z = (1 * 3 + Z * 3)
-35 + 8Z = (3 + 3Z)

Solving
-35 + 8Z = 3 + 3Z

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '-3Z' to each side of the equation.
-35 + 8Z + -3Z = 3 + 3Z + -3Z

Combine like terms: 8Z + -3Z = 5Z
-35 + 5Z = 3 + 3Z + -3Z

Combine like terms: 3Z + -3Z = 0
-35 + 5Z = 3 + 0
-35 + 5Z = 3

Add '35' to each side of the equation.
-35 + 35 + 5Z = 3 + 35

Combine like terms: -35 + 35 = 0
0 + 5Z = 3 + 35
5Z = 3 + 35

Combine like terms: 3 + 35 = 38
5Z = 38

Divide each side by '5'.
Z = 7.6

Simplifying
Z = 7.6`