3n^2-31n=-70

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Solution for 3n^2-31n=-70 equation:


Simplifying
3n2 + -31n = -70

Reorder the terms:
-31n + 3n2 = -70

Solving
-31n + 3n2 = -70

Solving for variable 'n'.

Reorder the terms:
70 + -31n + 3n2 = -70 + 70

Combine like terms: -70 + 70 = 0
70 + -31n + 3n2 = 0

Factor a trinomial.
(10 + -3n)(7 + -1n) = 0

Subproblem 1

Set the factor '(10 + -3n)' equal to zero and attempt to solve: Simplifying 10 + -3n = 0 Solving 10 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3n = 0 + -10 -3n = 0 + -10 Combine like terms: 0 + -10 = -10 -3n = -10 Divide each side by '-3'. n = 3.333333333 Simplifying n = 3.333333333

Subproblem 2

Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7

Solution

n = {3.333333333, 7}

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