7(z+1)-2(z-1)=2(z-1)+2(z-3)

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Solution for 7(z+1)-2(z-1)=2(z-1)+2(z-3) equation: 


Simplifying
7(z + 1) + -2(z + -1) = 2(z + -1) + 2(z + -3)

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

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

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

Combine like terms: 7 + 2 = 9
9 + 7z + -2z = 2(z + -1) + 2(z + -3)

Combine like terms: 7z + -2z = 5z
9 + 5z = 2(z + -1) + 2(z + -3)

Reorder the terms:
9 + 5z = 2(-1 + z) + 2(z + -3)
9 + 5z = (-1 * 2 + z * 2) + 2(z + -3)
9 + 5z = (-2 + 2z) + 2(z + -3)

Reorder the terms:
9 + 5z = -2 + 2z + 2(-3 + z)
9 + 5z = -2 + 2z + (-3 * 2 + z * 2)
9 + 5z = -2 + 2z + (-6 + 2z)

Reorder the terms:
9 + 5z = -2 + -6 + 2z + 2z

Combine like terms: -2 + -6 = -8
9 + 5z = -8 + 2z + 2z

Combine like terms: 2z + 2z = 4z
9 + 5z = -8 + 4z

Solving
9 + 5z = -8 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
9 + 5z + -4z = -8 + 4z + -4z

Combine like terms: 5z + -4z = 1z
9 + 1z = -8 + 4z + -4z

Combine like terms: 4z + -4z = 0
9 + 1z = -8 + 0
9 + 1z = -8

Add '-9' to each side of the equation.
9 + -9 + 1z = -8 + -9

Combine like terms: 9 + -9 = 0
0 + 1z = -8 + -9
1z = -8 + -9

Combine like terms: -8 + -9 = -17
1z = -17

Divide each side by '1'.
z = -17

Simplifying
z = -17

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