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

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Solution for 7(z+1)-2(z-1)=2(z+3)+(z-4) equation: 


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

Reorder the terms:
7(1 + z) + -2(z + -1) = 2(z + 3) + (z + -4)
(1 * 7 + z * 7) + -2(z + -1) = 2(z + 3) + (z + -4)
(7 + 7z) + -2(z + -1) = 2(z + 3) + (z + -4)

Reorder the terms:
7 + 7z + -2(-1 + z) = 2(z + 3) + (z + -4)
7 + 7z + (-1 * -2 + z * -2) = 2(z + 3) + (z + -4)
7 + 7z + (2 + -2z) = 2(z + 3) + (z + -4)

Reorder the terms:
7 + 2 + 7z + -2z = 2(z + 3) + (z + -4)

Combine like terms: 7 + 2 = 9
9 + 7z + -2z = 2(z + 3) + (z + -4)

Combine like terms: 7z + -2z = 5z
9 + 5z = 2(z + 3) + (z + -4)

Reorder the terms:
9 + 5z = 2(3 + z) + (z + -4)
9 + 5z = (3 * 2 + z * 2) + (z + -4)
9 + 5z = (6 + 2z) + (z + -4)

Reorder the terms:
9 + 5z = 6 + 2z + (-4 + z)

Remove parenthesis around (-4 + z)
9 + 5z = 6 + 2z + -4 + z

Reorder the terms:
9 + 5z = 6 + -4 + 2z + z

Combine like terms: 6 + -4 = 2
9 + 5z = 2 + 2z + z

Combine like terms: 2z + z = 3z
9 + 5z = 2 + 3z

Solving
9 + 5z = 2 + 3z

Solving for variable 'z'.

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

Add '-3z' to each side of the equation.
9 + 5z + -3z = 2 + 3z + -3z

Combine like terms: 5z + -3z = 2z
9 + 2z = 2 + 3z + -3z

Combine like terms: 3z + -3z = 0
9 + 2z = 2 + 0
9 + 2z = 2

Add '-9' to each side of the equation.
9 + -9 + 2z = 2 + -9

Combine like terms: 9 + -9 = 0
0 + 2z = 2 + -9
2z = 2 + -9

Combine like terms: 2 + -9 = -7
2z = -7

Divide each side by '2'.
z = -3.5

Simplifying
z = -3.5

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