13(z+1)-4(z-1)=4(z-4)+4(z-1)

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Solution for 13(z+1)-4(z-1)=4(z-4)+4(z-1) equation: 


Simplifying
13(z + 1) + -4(z + -1) = 4(z + -4) + 4(z + -1)

Reorder the terms:
13(1 + z) + -4(z + -1) = 4(z + -4) + 4(z + -1)
(1 * 13 + z * 13) + -4(z + -1) = 4(z + -4) + 4(z + -1)
(13 + 13z) + -4(z + -1) = 4(z + -4) + 4(z + -1)

Reorder the terms:
13 + 13z + -4(-1 + z) = 4(z + -4) + 4(z + -1)
13 + 13z + (-1 * -4 + z * -4) = 4(z + -4) + 4(z + -1)
13 + 13z + (4 + -4z) = 4(z + -4) + 4(z + -1)

Reorder the terms:
13 + 4 + 13z + -4z = 4(z + -4) + 4(z + -1)

Combine like terms: 13 + 4 = 17
17 + 13z + -4z = 4(z + -4) + 4(z + -1)

Combine like terms: 13z + -4z = 9z
17 + 9z = 4(z + -4) + 4(z + -1)

Reorder the terms:
17 + 9z = 4(-4 + z) + 4(z + -1)
17 + 9z = (-4 * 4 + z * 4) + 4(z + -1)
17 + 9z = (-16 + 4z) + 4(z + -1)

Reorder the terms:
17 + 9z = -16 + 4z + 4(-1 + z)
17 + 9z = -16 + 4z + (-1 * 4 + z * 4)
17 + 9z = -16 + 4z + (-4 + 4z)

Reorder the terms:
17 + 9z = -16 + -4 + 4z + 4z

Combine like terms: -16 + -4 = -20
17 + 9z = -20 + 4z + 4z

Combine like terms: 4z + 4z = 8z
17 + 9z = -20 + 8z

Solving
17 + 9z = -20 + 8z

Solving for variable 'z'.

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

Add '-8z' to each side of the equation.
17 + 9z + -8z = -20 + 8z + -8z

Combine like terms: 9z + -8z = 1z
17 + 1z = -20 + 8z + -8z

Combine like terms: 8z + -8z = 0
17 + 1z = -20 + 0
17 + 1z = -20

Add '-17' to each side of the equation.
17 + -17 + 1z = -20 + -17

Combine like terms: 17 + -17 = 0
0 + 1z = -20 + -17
1z = -20 + -17

Combine like terms: -20 + -17 = -37
1z = -37

Divide each side by '1'.
z = -37

Simplifying
z = -37

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