10n^2+38n=3n

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Solution for 10n^2+38n=3n equation:


Simplifying
10n2 + 38n = 3n

Reorder the terms:
38n + 10n2 = 3n

Solving
38n + 10n2 = 3n

Solving for variable 'n'.

Reorder the terms:
38n + -3n + 10n2 = 3n + -3n

Combine like terms: 38n + -3n = 35n
35n + 10n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
35n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5n'.
5n(7 + 2n) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(7 + 2n)' equal to zero and attempt to solve: Simplifying 7 + 2n = 0 Solving 7 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n = 0 + -7 2n = 0 + -7 Combine like terms: 0 + -7 = -7 2n = -7 Divide each side by '2'. n = -3.5 Simplifying n = -3.5

Solution

n = {0, -3.5}

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