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

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Solution for 10(z+2)-2(z-4)=(z-2)+3(z-2) equation: 


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

Reorder the terms:
10(2 + z) + -2(z + -4) = (z + -2) + 3(z + -2)
(2 * 10 + z * 10) + -2(z + -4) = (z + -2) + 3(z + -2)
(20 + 10z) + -2(z + -4) = (z + -2) + 3(z + -2)

Reorder the terms:
20 + 10z + -2(-4 + z) = (z + -2) + 3(z + -2)
20 + 10z + (-4 * -2 + z * -2) = (z + -2) + 3(z + -2)
20 + 10z + (8 + -2z) = (z + -2) + 3(z + -2)

Reorder the terms:
20 + 8 + 10z + -2z = (z + -2) + 3(z + -2)

Combine like terms: 20 + 8 = 28
28 + 10z + -2z = (z + -2) + 3(z + -2)

Combine like terms: 10z + -2z = 8z
28 + 8z = (z + -2) + 3(z + -2)

Reorder the terms:
28 + 8z = (-2 + z) + 3(z + -2)

Remove parenthesis around (-2 + z)
28 + 8z = -2 + z + 3(z + -2)

Reorder the terms:
28 + 8z = -2 + z + 3(-2 + z)
28 + 8z = -2 + z + (-2 * 3 + z * 3)
28 + 8z = -2 + z + (-6 + 3z)

Reorder the terms:
28 + 8z = -2 + -6 + z + 3z

Combine like terms: -2 + -6 = -8
28 + 8z = -8 + z + 3z

Combine like terms: z + 3z = 4z
28 + 8z = -8 + 4z

Solving
28 + 8z = -8 + 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.
28 + 8z + -4z = -8 + 4z + -4z

Combine like terms: 8z + -4z = 4z
28 + 4z = -8 + 4z + -4z

Combine like terms: 4z + -4z = 0
28 + 4z = -8 + 0
28 + 4z = -8

Add '-28' to each side of the equation.
28 + -28 + 4z = -8 + -28

Combine like terms: 28 + -28 = 0
0 + 4z = -8 + -28
4z = -8 + -28

Combine like terms: -8 + -28 = -36
4z = -36

Divide each side by '4'.
z = -9

Simplifying
z = -9

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