4n^2+2n-30=0

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Solution for 4n^2+2n-30=0 equation:


Simplifying
4n2 + 2n + -30 = 0

Reorder the terms:
-30 + 2n + 4n2 = 0

Solving
-30 + 2n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + n + 2n2) = 0

Factor a trinomial.
2((-3 + -1n)(5 + -2n)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3

Subproblem 2

Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 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 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5

Solution

n = {-3, 2.5}

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