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

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Solution for 10(z+1)-2(z-2)=3(z-2)+(z-4) equation: 


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

Reorder the terms:
10(1 + z) + -2(z + -2) = 3(z + -2) + (z + -4)
(1 * 10 + z * 10) + -2(z + -2) = 3(z + -2) + (z + -4)
(10 + 10z) + -2(z + -2) = 3(z + -2) + (z + -4)

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

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

Combine like terms: 10 + 4 = 14
14 + 10z + -2z = 3(z + -2) + (z + -4)

Combine like terms: 10z + -2z = 8z
14 + 8z = 3(z + -2) + (z + -4)

Reorder the terms:
14 + 8z = 3(-2 + z) + (z + -4)
14 + 8z = (-2 * 3 + z * 3) + (z + -4)
14 + 8z = (-6 + 3z) + (z + -4)

Reorder the terms:
14 + 8z = -6 + 3z + (-4 + z)

Remove parenthesis around (-4 + z)
14 + 8z = -6 + 3z + -4 + z

Reorder the terms:
14 + 8z = -6 + -4 + 3z + z

Combine like terms: -6 + -4 = -10
14 + 8z = -10 + 3z + z

Combine like terms: 3z + z = 4z
14 + 8z = -10 + 4z

Solving
14 + 8z = -10 + 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.
14 + 8z + -4z = -10 + 4z + -4z

Combine like terms: 8z + -4z = 4z
14 + 4z = -10 + 4z + -4z

Combine like terms: 4z + -4z = 0
14 + 4z = -10 + 0
14 + 4z = -10

Add '-14' to each side of the equation.
14 + -14 + 4z = -10 + -14

Combine like terms: 14 + -14 = 0
0 + 4z = -10 + -14
4z = -10 + -14

Combine like terms: -10 + -14 = -24
4z = -24

Divide each side by '4'.
z = -6

Simplifying
z = -6

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