10n^2-4=3n

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Solution for 10n^2-4=3n equation:


Simplifying
10n2 + -4 = 3n

Reorder the terms:
-4 + 10n2 = 3n

Solving
-4 + 10n2 = 3n

Solving for variable 'n'.

Reorder the terms:
-4 + -3n + 10n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-4 + -3n + 10n2 = 0

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

Subproblem 1

Set the factor '(-1 + -2n)' equal to zero and attempt to solve: Simplifying -1 + -2n = 0 Solving -1 + -2n = 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 + -2n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2n = 0 + 1 -2n = 0 + 1 Combine like terms: 0 + 1 = 1 -2n = 1 Divide each side by '-2'. n = -0.5 Simplifying n = -0.5

Subproblem 2

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

Solution

n = {-0.5, 0.8}

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