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

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Solution for 100(z+3)-3(z-1)=4(z-3)+(z-1) equation: 


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

Reorder the terms:
100(3 + z) + -3(z + -1) = 4(z + -3) + (z + -1)
(3 * 100 + z * 100) + -3(z + -1) = 4(z + -3) + (z + -1)
(300 + 100z) + -3(z + -1) = 4(z + -3) + (z + -1)

Reorder the terms:
300 + 100z + -3(-1 + z) = 4(z + -3) + (z + -1)
300 + 100z + (-1 * -3 + z * -3) = 4(z + -3) + (z + -1)
300 + 100z + (3 + -3z) = 4(z + -3) + (z + -1)

Reorder the terms:
300 + 3 + 100z + -3z = 4(z + -3) + (z + -1)

Combine like terms: 300 + 3 = 303
303 + 100z + -3z = 4(z + -3) + (z + -1)

Combine like terms: 100z + -3z = 97z
303 + 97z = 4(z + -3) + (z + -1)

Reorder the terms:
303 + 97z = 4(-3 + z) + (z + -1)
303 + 97z = (-3 * 4 + z * 4) + (z + -1)
303 + 97z = (-12 + 4z) + (z + -1)

Reorder the terms:
303 + 97z = -12 + 4z + (-1 + z)

Remove parenthesis around (-1 + z)
303 + 97z = -12 + 4z + -1 + z

Reorder the terms:
303 + 97z = -12 + -1 + 4z + z

Combine like terms: -12 + -1 = -13
303 + 97z = -13 + 4z + z

Combine like terms: 4z + z = 5z
303 + 97z = -13 + 5z

Solving
303 + 97z = -13 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
303 + 97z + -5z = -13 + 5z + -5z

Combine like terms: 97z + -5z = 92z
303 + 92z = -13 + 5z + -5z

Combine like terms: 5z + -5z = 0
303 + 92z = -13 + 0
303 + 92z = -13

Add '-303' to each side of the equation.
303 + -303 + 92z = -13 + -303

Combine like terms: 303 + -303 = 0
0 + 92z = -13 + -303
92z = -13 + -303

Combine like terms: -13 + -303 = -316
92z = -316

Divide each side by '92'.
z = -3.434782609

Simplifying
z = -3.434782609

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