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

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Solution for 8(z+1)-3(z-1)=2(z-2)+2(z-4) equation: 


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

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

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

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

Combine like terms: 8 + 3 = 11
11 + 8z + -3z = 2(z + -2) + 2(z + -4)

Combine like terms: 8z + -3z = 5z
11 + 5z = 2(z + -2) + 2(z + -4)

Reorder the terms:
11 + 5z = 2(-2 + z) + 2(z + -4)
11 + 5z = (-2 * 2 + z * 2) + 2(z + -4)
11 + 5z = (-4 + 2z) + 2(z + -4)

Reorder the terms:
11 + 5z = -4 + 2z + 2(-4 + z)
11 + 5z = -4 + 2z + (-4 * 2 + z * 2)
11 + 5z = -4 + 2z + (-8 + 2z)

Reorder the terms:
11 + 5z = -4 + -8 + 2z + 2z

Combine like terms: -4 + -8 = -12
11 + 5z = -12 + 2z + 2z

Combine like terms: 2z + 2z = 4z
11 + 5z = -12 + 4z

Solving
11 + 5z = -12 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
11 + 5z + -4z = -12 + 4z + -4z

Combine like terms: 5z + -4z = 1z
11 + 1z = -12 + 4z + -4z

Combine like terms: 4z + -4z = 0
11 + 1z = -12 + 0
11 + 1z = -12

Add '-11' to each side of the equation.
11 + -11 + 1z = -12 + -11

Combine like terms: 11 + -11 = 0
0 + 1z = -12 + -11
1z = -12 + -11

Combine like terms: -12 + -11 = -23
1z = -23

Divide each side by '1'.
z = -23

Simplifying
z = -23

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