13(z+1)-4(z-4)=4(z-3)+4(z-1)

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Solution for 13(z+1)-4(z-4)=4(z-3)+4(z-1) equation: 


Simplifying
13(z + 1) + -4(z + -4) = 4(z + -3) + 4(z + -1)

Reorder the terms:
13(1 + z) + -4(z + -4) = 4(z + -3) + 4(z + -1)
(1 * 13 + z * 13) + -4(z + -4) = 4(z + -3) + 4(z + -1)
(13 + 13z) + -4(z + -4) = 4(z + -3) + 4(z + -1)

Reorder the terms:
13 + 13z + -4(-4 + z) = 4(z + -3) + 4(z + -1)
13 + 13z + (-4 * -4 + z * -4) = 4(z + -3) + 4(z + -1)
13 + 13z + (16 + -4z) = 4(z + -3) + 4(z + -1)

Reorder the terms:
13 + 16 + 13z + -4z = 4(z + -3) + 4(z + -1)

Combine like terms: 13 + 16 = 29
29 + 13z + -4z = 4(z + -3) + 4(z + -1)

Combine like terms: 13z + -4z = 9z
29 + 9z = 4(z + -3) + 4(z + -1)

Reorder the terms:
29 + 9z = 4(-3 + z) + 4(z + -1)
29 + 9z = (-3 * 4 + z * 4) + 4(z + -1)
29 + 9z = (-12 + 4z) + 4(z + -1)

Reorder the terms:
29 + 9z = -12 + 4z + 4(-1 + z)
29 + 9z = -12 + 4z + (-1 * 4 + z * 4)
29 + 9z = -12 + 4z + (-4 + 4z)

Reorder the terms:
29 + 9z = -12 + -4 + 4z + 4z

Combine like terms: -12 + -4 = -16
29 + 9z = -16 + 4z + 4z

Combine like terms: 4z + 4z = 8z
29 + 9z = -16 + 8z

Solving
29 + 9z = -16 + 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.
29 + 9z + -8z = -16 + 8z + -8z

Combine like terms: 9z + -8z = 1z
29 + 1z = -16 + 8z + -8z

Combine like terms: 8z + -8z = 0
29 + 1z = -16 + 0
29 + 1z = -16

Add '-29' to each side of the equation.
29 + -29 + 1z = -16 + -29

Combine like terms: 29 + -29 = 0
0 + 1z = -16 + -29
1z = -16 + -29

Combine like terms: -16 + -29 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45

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