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

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


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

Reorder the terms:
13(3 + z) + -4(z + -1) = 4(z + -3) + 4(z + -4)
(3 * 13 + z * 13) + -4(z + -1) = 4(z + -3) + 4(z + -4)
(39 + 13z) + -4(z + -1) = 4(z + -3) + 4(z + -4)

Reorder the terms:
39 + 13z + -4(-1 + z) = 4(z + -3) + 4(z + -4)
39 + 13z + (-1 * -4 + z * -4) = 4(z + -3) + 4(z + -4)
39 + 13z + (4 + -4z) = 4(z + -3) + 4(z + -4)

Reorder the terms:
39 + 4 + 13z + -4z = 4(z + -3) + 4(z + -4)

Combine like terms: 39 + 4 = 43
43 + 13z + -4z = 4(z + -3) + 4(z + -4)

Combine like terms: 13z + -4z = 9z
43 + 9z = 4(z + -3) + 4(z + -4)

Reorder the terms:
43 + 9z = 4(-3 + z) + 4(z + -4)
43 + 9z = (-3 * 4 + z * 4) + 4(z + -4)
43 + 9z = (-12 + 4z) + 4(z + -4)

Reorder the terms:
43 + 9z = -12 + 4z + 4(-4 + z)
43 + 9z = -12 + 4z + (-4 * 4 + z * 4)
43 + 9z = -12 + 4z + (-16 + 4z)

Reorder the terms:
43 + 9z = -12 + -16 + 4z + 4z

Combine like terms: -12 + -16 = -28
43 + 9z = -28 + 4z + 4z

Combine like terms: 4z + 4z = 8z
43 + 9z = -28 + 8z

Solving
43 + 9z = -28 + 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.
43 + 9z + -8z = -28 + 8z + -8z

Combine like terms: 9z + -8z = 1z
43 + 1z = -28 + 8z + -8z

Combine like terms: 8z + -8z = 0
43 + 1z = -28 + 0
43 + 1z = -28

Add '-43' to each side of the equation.
43 + -43 + 1z = -28 + -43

Combine like terms: 43 + -43 = 0
0 + 1z = -28 + -43
1z = -28 + -43

Combine like terms: -28 + -43 = -71
1z = -71

Divide each side by '1'.
z = -71

Simplifying
z = -71

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