3n^2-55=1-17n

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Solution for 3n^2-55=1-17n equation:


Simplifying
3n2 + -55 = 1 + -17n

Reorder the terms:
-55 + 3n2 = 1 + -17n

Solving
-55 + 3n2 = 1 + -17n

Solving for variable 'n'.

Reorder the terms:
-55 + -1 + 17n + 3n2 = 1 + -17n + -1 + 17n

Combine like terms: -55 + -1 = -56
-56 + 17n + 3n2 = 1 + -17n + -1 + 17n

Reorder the terms:
-56 + 17n + 3n2 = 1 + -1 + -17n + 17n

Combine like terms: 1 + -1 = 0
-56 + 17n + 3n2 = 0 + -17n + 17n
-56 + 17n + 3n2 = -17n + 17n

Combine like terms: -17n + 17n = 0
-56 + 17n + 3n2 = 0

Factor a trinomial.
(-8 + -1n)(7 + -3n) = 0

Subproblem 1

Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8

Subproblem 2

Set the factor '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333

Solution

n = {-8, 2.333333333}

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