3n^2+5=8n

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Solution for 3n^2+5=8n equation:


Simplifying
3n2 + 5 = 8n

Reorder the terms:
5 + 3n2 = 8n

Solving
5 + 3n2 = 8n

Solving for variable 'n'.

Reorder the terms:
5 + -8n + 3n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
5 + -8n + 3n2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667

Solution

n = {1, 1.666666667}

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