3n^2=4-11n

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Solution for 3n^2=4-11n equation:


Simplifying
3n2 = 4 + -11n

Solving
3n2 = 4 + -11n

Solving for variable 'n'.

Reorder the terms:
-4 + 11n + 3n2 = 4 + -11n + -4 + 11n

Reorder the terms:
-4 + 11n + 3n2 = 4 + -4 + -11n + 11n

Combine like terms: 4 + -4 = 0
-4 + 11n + 3n2 = 0 + -11n + 11n
-4 + 11n + 3n2 = -11n + 11n

Combine like terms: -11n + 11n = 0
-4 + 11n + 3n2 = 0

Factor a trinomial.
(-4 + -1n)(1 + -3n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333

Solution

n = {-4, 0.3333333333}

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