30n^2+55n-10=0

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Solution for 30n^2+55n-10=0 equation:


Simplifying
30n2 + 55n + -10 = 0

Reorder the terms:
-10 + 55n + 30n2 = 0

Solving
-10 + 55n + 30n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 11n + 6n2) = 0

Factor a trinomial.
5((-2 + -1n)(1 + -6n)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -6n)' equal to zero and attempt to solve: Simplifying 1 + -6n = 0 Solving 1 + -6n = 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 + -6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6n = 0 + -1 -6n = 0 + -1 Combine like terms: 0 + -1 = -1 -6n = -1 Divide each side by '-6'. n = 0.1666666667 Simplifying n = 0.1666666667

Solution

n = {-2, 0.1666666667}

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