5n^2-8=6n

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Solution for 5n^2-8=6n equation:


Simplifying
5n2 + -8 = 6n

Reorder the terms:
-8 + 5n2 = 6n

Solving
-8 + 5n2 = 6n

Solving for variable 'n'.

Reorder the terms:
-8 + -6n + 5n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-8 + -6n + 5n2 = 0

Factor a trinomial.
(-4 + -5n)(2 + -1n) = 0

Subproblem 1

Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 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 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8

Subproblem 2

Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2

Solution

n = {-0.8, 2}

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