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

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


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

Reorder the terms:
8(2 + z) + -2(z + -4) = 2(z + -2) + 3(z + -2)
(2 * 8 + z * 8) + -2(z + -4) = 2(z + -2) + 3(z + -2)
(16 + 8z) + -2(z + -4) = 2(z + -2) + 3(z + -2)

Reorder the terms:
16 + 8z + -2(-4 + z) = 2(z + -2) + 3(z + -2)
16 + 8z + (-4 * -2 + z * -2) = 2(z + -2) + 3(z + -2)
16 + 8z + (8 + -2z) = 2(z + -2) + 3(z + -2)

Reorder the terms:
16 + 8 + 8z + -2z = 2(z + -2) + 3(z + -2)

Combine like terms: 16 + 8 = 24
24 + 8z + -2z = 2(z + -2) + 3(z + -2)

Combine like terms: 8z + -2z = 6z
24 + 6z = 2(z + -2) + 3(z + -2)

Reorder the terms:
24 + 6z = 2(-2 + z) + 3(z + -2)
24 + 6z = (-2 * 2 + z * 2) + 3(z + -2)
24 + 6z = (-4 + 2z) + 3(z + -2)

Reorder the terms:
24 + 6z = -4 + 2z + 3(-2 + z)
24 + 6z = -4 + 2z + (-2 * 3 + z * 3)
24 + 6z = -4 + 2z + (-6 + 3z)

Reorder the terms:
24 + 6z = -4 + -6 + 2z + 3z

Combine like terms: -4 + -6 = -10
24 + 6z = -10 + 2z + 3z

Combine like terms: 2z + 3z = 5z
24 + 6z = -10 + 5z

Solving
24 + 6z = -10 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
24 + 6z + -5z = -10 + 5z + -5z

Combine like terms: 6z + -5z = 1z
24 + 1z = -10 + 5z + -5z

Combine like terms: 5z + -5z = 0
24 + 1z = -10 + 0
24 + 1z = -10

Add '-24' to each side of the equation.
24 + -24 + 1z = -10 + -24

Combine like terms: 24 + -24 = 0
0 + 1z = -10 + -24
1z = -10 + -24

Combine like terms: -10 + -24 = -34
1z = -34

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

Simplifying
z = -34

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