6n^2-110=-8n

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Solution for 6n^2-110=-8n equation:


Simplifying
6n2 + -110 = -8n

Reorder the terms:
-110 + 6n2 = -8n

Solving
-110 + 6n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-110 + 8n + 6n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-110 + 8n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 4n + 3n2) = 0

Factor a trinomial.
2((-5 + -1n)(11 + -3n)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(11 + -3n)' equal to zero and attempt to solve: Simplifying 11 + -3n = 0 Solving 11 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3n = 0 + -11 -3n = 0 + -11 Combine like terms: 0 + -11 = -11 -3n = -11 Divide each side by '-3'. n = 3.666666667 Simplifying n = 3.666666667

Solution

n = {-5, 3.666666667}

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