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

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


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

Reorder the terms:
10(3 + z) + -3(z + -2) = 2(z + -2) + 4(z + -1)
(3 * 10 + z * 10) + -3(z + -2) = 2(z + -2) + 4(z + -1)
(30 + 10z) + -3(z + -2) = 2(z + -2) + 4(z + -1)

Reorder the terms:
30 + 10z + -3(-2 + z) = 2(z + -2) + 4(z + -1)
30 + 10z + (-2 * -3 + z * -3) = 2(z + -2) + 4(z + -1)
30 + 10z + (6 + -3z) = 2(z + -2) + 4(z + -1)

Reorder the terms:
30 + 6 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 30 + 6 = 36
36 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 10z + -3z = 7z
36 + 7z = 2(z + -2) + 4(z + -1)

Reorder the terms:
36 + 7z = 2(-2 + z) + 4(z + -1)
36 + 7z = (-2 * 2 + z * 2) + 4(z + -1)
36 + 7z = (-4 + 2z) + 4(z + -1)

Reorder the terms:
36 + 7z = -4 + 2z + 4(-1 + z)
36 + 7z = -4 + 2z + (-1 * 4 + z * 4)
36 + 7z = -4 + 2z + (-4 + 4z)

Reorder the terms:
36 + 7z = -4 + -4 + 2z + 4z

Combine like terms: -4 + -4 = -8
36 + 7z = -8 + 2z + 4z

Combine like terms: 2z + 4z = 6z
36 + 7z = -8 + 6z

Solving
36 + 7z = -8 + 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.
36 + 7z + -6z = -8 + 6z + -6z

Combine like terms: 7z + -6z = 1z
36 + 1z = -8 + 6z + -6z

Combine like terms: 6z + -6z = 0
36 + 1z = -8 + 0
36 + 1z = -8

Add '-36' to each side of the equation.
36 + -36 + 1z = -8 + -36

Combine like terms: 36 + -36 = 0
0 + 1z = -8 + -36
1z = -8 + -36

Combine like terms: -8 + -36 = -44
1z = -44

Divide each side by '1'.
z = -44

Simplifying
z = -44

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