3n^2-80=-8n

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Solution for 3n^2-80=-8n equation:


Simplifying
3n2 + -80 = -8n

Reorder the terms:
-80 + 3n2 = -8n

Solving
-80 + 3n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-80 + 8n + 3n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-80 + 8n + 3n2 = 0

Factor a trinomial.
(-20 + -3n)(4 + -1n) = 0

Subproblem 1

Set the factor '(-20 + -3n)' equal to zero and attempt to solve: Simplifying -20 + -3n = 0 Solving -20 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -3n = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3n = 0 + 20 -3n = 0 + 20 Combine like terms: 0 + 20 = 20 -3n = 20 Divide each side by '-3'. n = -6.666666667 Simplifying n = -6.666666667

Subproblem 2

Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Solution

n = {-6.666666667, 4}

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