56n^2+160=-204n

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Solution for 56n^2+160=-204n equation:


Simplifying
56n2 + 160 = -204n

Reorder the terms:
160 + 56n2 = -204n

Solving
160 + 56n2 = -204n

Solving for variable 'n'.

Reorder the terms:
160 + 204n + 56n2 = -204n + 204n

Combine like terms: -204n + 204n = 0
160 + 204n + 56n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + 51n + 14n2) = 0

Factor a trinomial.
4((5 + 2n)(8 + 7n)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(8 + 7n)' equal to zero and attempt to solve: Simplifying 8 + 7n = 0 Solving 8 + 7n = 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 + 7n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7n = 0 + -8 7n = 0 + -8 Combine like terms: 0 + -8 = -8 7n = -8 Divide each side by '7'. n = -1.142857143 Simplifying n = -1.142857143

Solution

n = {-2.5, -1.142857143}

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