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

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


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

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

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

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

Combine like terms: 40 + 3 = 43
43 + 10z + -3z = 3(z + -1) + 3(z + -2)

Combine like terms: 10z + -3z = 7z
43 + 7z = 3(z + -1) + 3(z + -2)

Reorder the terms:
43 + 7z = 3(-1 + z) + 3(z + -2)
43 + 7z = (-1 * 3 + z * 3) + 3(z + -2)
43 + 7z = (-3 + 3z) + 3(z + -2)

Reorder the terms:
43 + 7z = -3 + 3z + 3(-2 + z)
43 + 7z = -3 + 3z + (-2 * 3 + z * 3)
43 + 7z = -3 + 3z + (-6 + 3z)

Reorder the terms:
43 + 7z = -3 + -6 + 3z + 3z

Combine like terms: -3 + -6 = -9
43 + 7z = -9 + 3z + 3z

Combine like terms: 3z + 3z = 6z
43 + 7z = -9 + 6z

Solving
43 + 7z = -9 + 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.
43 + 7z + -6z = -9 + 6z + -6z

Combine like terms: 7z + -6z = 1z
43 + 1z = -9 + 6z + -6z

Combine like terms: 6z + -6z = 0
43 + 1z = -9 + 0
43 + 1z = -9

Add '-43' to each side of the equation.
43 + -43 + 1z = -9 + -43

Combine like terms: 43 + -43 = 0
0 + 1z = -9 + -43
1z = -9 + -43

Combine like terms: -9 + -43 = -52
1z = -52

Divide each side by '1'.
z = -52

Simplifying
z = -52

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