3n^2-8n-51=0

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Solution for 3n^2-8n-51=0 equation:


Simplifying
3n2 + -8n + -51 = 0

Reorder the terms:
-51 + -8n + 3n2 = 0

Solving
-51 + -8n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(17 + -3n) = 0

Subproblem 1

Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3

Subproblem 2

Set the factor '(17 + -3n)' equal to zero and attempt to solve: Simplifying 17 + -3n = 0 Solving 17 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3n = 0 + -17 -3n = 0 + -17 Combine like terms: 0 + -17 = -17 -3n = -17 Divide each side by '-3'. n = 5.666666667 Simplifying n = 5.666666667

Solution

n = {-3, 5.666666667}

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