6-n+8=3(n-5)+5(-4n-7)

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Solution for 6-n+8=3(n-5)+5(-4n-7) equation:


Simplifying
6 + -1n + 8 = 3(n + -5) + 5(-4n + -7)

Reorder the terms:
6 + 8 + -1n = 3(n + -5) + 5(-4n + -7)

Combine like terms: 6 + 8 = 14
14 + -1n = 3(n + -5) + 5(-4n + -7)

Reorder the terms:
14 + -1n = 3(-5 + n) + 5(-4n + -7)
14 + -1n = (-5 * 3 + n * 3) + 5(-4n + -7)
14 + -1n = (-15 + 3n) + 5(-4n + -7)

Reorder the terms:
14 + -1n = -15 + 3n + 5(-7 + -4n)
14 + -1n = -15 + 3n + (-7 * 5 + -4n * 5)
14 + -1n = -15 + 3n + (-35 + -20n)

Reorder the terms:
14 + -1n = -15 + -35 + 3n + -20n

Combine like terms: -15 + -35 = -50
14 + -1n = -50 + 3n + -20n

Combine like terms: 3n + -20n = -17n
14 + -1n = -50 + -17n

Solving
14 + -1n = -50 + -17n

Solving for variable 'n'.

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

Add '17n' to each side of the equation.
14 + -1n + 17n = -50 + -17n + 17n

Combine like terms: -1n + 17n = 16n
14 + 16n = -50 + -17n + 17n

Combine like terms: -17n + 17n = 0
14 + 16n = -50 + 0
14 + 16n = -50

Add '-14' to each side of the equation.
14 + -14 + 16n = -50 + -14

Combine like terms: 14 + -14 = 0
0 + 16n = -50 + -14
16n = -50 + -14

Combine like terms: -50 + -14 = -64
16n = -64

Divide each side by '16'.
n = -4

Simplifying
n = -4

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