5n^2+20n-162=-2

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Solution for 5n^2+20n-162=-2 equation:


Simplifying
5n2 + 20n + -162 = -2

Reorder the terms:
-162 + 20n + 5n2 = -2

Solving
-162 + 20n + 5n2 = -2

Solving for variable 'n'.

Reorder the terms:
-162 + 2 + 20n + 5n2 = -2 + 2

Combine like terms: -162 + 2 = -160
-160 + 20n + 5n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-160 + 20n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-32 + 4n + n2) = 0

Factor a trinomial.
5((-8 + -1n)(4 + -1n)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8

Subproblem 2

Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 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 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Solution

n = {-8, 4}

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