n(3n-2)=40

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Solution for n(3n-2)=40 equation:


Simplifying
n(3n + -2) = 40

Reorder the terms:
n(-2 + 3n) = 40
(-2 * n + 3n * n) = 40
(-2n + 3n2) = 40

Solving
-2n + 3n2 = 40

Solving for variable 'n'.

Reorder the terms:
-40 + -2n + 3n2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -2n + 3n2 = 0

Factor a trinomial.
(-10 + -3n)(4 + -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 '(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 = {-3.333333333, 4}

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