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

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


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

Reorder the terms:
10(4 + z) + -2(z + -2) = 4(z + -4) + (z + -4)
(4 * 10 + z * 10) + -2(z + -2) = 4(z + -4) + (z + -4)
(40 + 10z) + -2(z + -2) = 4(z + -4) + (z + -4)

Reorder the terms:
40 + 10z + -2(-2 + z) = 4(z + -4) + (z + -4)
40 + 10z + (-2 * -2 + z * -2) = 4(z + -4) + (z + -4)
40 + 10z + (4 + -2z) = 4(z + -4) + (z + -4)

Reorder the terms:
40 + 4 + 10z + -2z = 4(z + -4) + (z + -4)

Combine like terms: 40 + 4 = 44
44 + 10z + -2z = 4(z + -4) + (z + -4)

Combine like terms: 10z + -2z = 8z
44 + 8z = 4(z + -4) + (z + -4)

Reorder the terms:
44 + 8z = 4(-4 + z) + (z + -4)
44 + 8z = (-4 * 4 + z * 4) + (z + -4)
44 + 8z = (-16 + 4z) + (z + -4)

Reorder the terms:
44 + 8z = -16 + 4z + (-4 + z)

Remove parenthesis around (-4 + z)
44 + 8z = -16 + 4z + -4 + z

Reorder the terms:
44 + 8z = -16 + -4 + 4z + z

Combine like terms: -16 + -4 = -20
44 + 8z = -20 + 4z + z

Combine like terms: 4z + z = 5z
44 + 8z = -20 + 5z

Solving
44 + 8z = -20 + 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.
44 + 8z + -5z = -20 + 5z + -5z

Combine like terms: 8z + -5z = 3z
44 + 3z = -20 + 5z + -5z

Combine like terms: 5z + -5z = 0
44 + 3z = -20 + 0
44 + 3z = -20

Add '-44' to each side of the equation.
44 + -44 + 3z = -20 + -44

Combine like terms: 44 + -44 = 0
0 + 3z = -20 + -44
3z = -20 + -44

Combine like terms: -20 + -44 = -64
3z = -64

Divide each side by '3'.
z = -21.33333333

Simplifying
z = -21.33333333

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