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

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


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

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

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

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

Combine like terms: 10 + 3 = 13
13 + 10z + -3z = 4(z + -4) + 2(z + -2)

Combine like terms: 10z + -3z = 7z
13 + 7z = 4(z + -4) + 2(z + -2)

Reorder the terms:
13 + 7z = 4(-4 + z) + 2(z + -2)
13 + 7z = (-4 * 4 + z * 4) + 2(z + -2)
13 + 7z = (-16 + 4z) + 2(z + -2)

Reorder the terms:
13 + 7z = -16 + 4z + 2(-2 + z)
13 + 7z = -16 + 4z + (-2 * 2 + z * 2)
13 + 7z = -16 + 4z + (-4 + 2z)

Reorder the terms:
13 + 7z = -16 + -4 + 4z + 2z

Combine like terms: -16 + -4 = -20
13 + 7z = -20 + 4z + 2z

Combine like terms: 4z + 2z = 6z
13 + 7z = -20 + 6z

Solving
13 + 7z = -20 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
13 + 7z + -6z = -20 + 6z + -6z

Combine like terms: 7z + -6z = 1z
13 + 1z = -20 + 6z + -6z

Combine like terms: 6z + -6z = 0
13 + 1z = -20 + 0
13 + 1z = -20

Add '-13' to each side of the equation.
13 + -13 + 1z = -20 + -13

Combine like terms: 13 + -13 = 0
0 + 1z = -20 + -13
1z = -20 + -13

Combine like terms: -20 + -13 = -33
1z = -33

Divide each side by '1'.
z = -33

Simplifying
z = -33

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