0=2n^3+24n^2+70n

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Solution for 0=2n^3+24n^2+70n equation:


Simplifying
0 = 2n3 + 24n2 + 70n

Reorder the terms:
0 = 70n + 24n2 + 2n3

Solving
0 = 70n + 24n2 + 2n3

Solving for variable 'n'.
Remove the zero:
-70n + -24n2 + -2n3 = 70n + 24n2 + 2n3 + -70n + -24n2 + -2n3

Reorder the terms:
-70n + -24n2 + -2n3 = 70n + -70n + 24n2 + -24n2 + 2n3 + -2n3

Combine like terms: 70n + -70n = 0
-70n + -24n2 + -2n3 = 0 + 24n2 + -24n2 + 2n3 + -2n3
-70n + -24n2 + -2n3 = 24n2 + -24n2 + 2n3 + -2n3

Combine like terms: 24n2 + -24n2 = 0
-70n + -24n2 + -2n3 = 0 + 2n3 + -2n3
-70n + -24n2 + -2n3 = 2n3 + -2n3

Combine like terms: 2n3 + -2n3 = 0
-70n + -24n2 + -2n3 = 0

Factor out the Greatest Common Factor (GCF), '-2n'.
-2n(35 + 12n + n2) = 0

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

Ignore the factor -2.

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 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 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 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7

Subproblem 3

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Solution

n = {0, -7, -5}

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