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

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


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

Reorder the terms:
10(4 + z) + -3(z + -2) = 3(z + -3) + 3(z + -1)
(4 * 10 + z * 10) + -3(z + -2) = 3(z + -3) + 3(z + -1)
(40 + 10z) + -3(z + -2) = 3(z + -3) + 3(z + -1)

Reorder the terms:
40 + 10z + -3(-2 + z) = 3(z + -3) + 3(z + -1)
40 + 10z + (-2 * -3 + z * -3) = 3(z + -3) + 3(z + -1)
40 + 10z + (6 + -3z) = 3(z + -3) + 3(z + -1)

Reorder the terms:
40 + 6 + 10z + -3z = 3(z + -3) + 3(z + -1)

Combine like terms: 40 + 6 = 46
46 + 10z + -3z = 3(z + -3) + 3(z + -1)

Combine like terms: 10z + -3z = 7z
46 + 7z = 3(z + -3) + 3(z + -1)

Reorder the terms:
46 + 7z = 3(-3 + z) + 3(z + -1)
46 + 7z = (-3 * 3 + z * 3) + 3(z + -1)
46 + 7z = (-9 + 3z) + 3(z + -1)

Reorder the terms:
46 + 7z = -9 + 3z + 3(-1 + z)
46 + 7z = -9 + 3z + (-1 * 3 + z * 3)
46 + 7z = -9 + 3z + (-3 + 3z)

Reorder the terms:
46 + 7z = -9 + -3 + 3z + 3z

Combine like terms: -9 + -3 = -12
46 + 7z = -12 + 3z + 3z

Combine like terms: 3z + 3z = 6z
46 + 7z = -12 + 6z

Solving
46 + 7z = -12 + 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.
46 + 7z + -6z = -12 + 6z + -6z

Combine like terms: 7z + -6z = 1z
46 + 1z = -12 + 6z + -6z

Combine like terms: 6z + -6z = 0
46 + 1z = -12 + 0
46 + 1z = -12

Add '-46' to each side of the equation.
46 + -46 + 1z = -12 + -46

Combine like terms: 46 + -46 = 0
0 + 1z = -12 + -46
1z = -12 + -46

Combine like terms: -12 + -46 = -58
1z = -58

Divide each side by '1'.
z = -58

Simplifying
z = -58

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