0=-3n^2+22+5n

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Solution for 0=-3n^2+22+5n equation:


Simplifying
0 = -3n2 + 22 + 5n

Reorder the terms:
0 = 22 + 5n + -3n2

Solving
0 = 22 + 5n + -3n2

Solving for variable 'n'.

Combine like terms: 0 + -22 = -22
-22 + -5n + 3n2 = 22 + 5n + -3n2 + -22 + -5n + 3n2

Reorder the terms:
-22 + -5n + 3n2 = 22 + -22 + 5n + -5n + -3n2 + 3n2

Combine like terms: 22 + -22 = 0
-22 + -5n + 3n2 = 0 + 5n + -5n + -3n2 + 3n2
-22 + -5n + 3n2 = 5n + -5n + -3n2 + 3n2

Combine like terms: 5n + -5n = 0
-22 + -5n + 3n2 = 0 + -3n2 + 3n2
-22 + -5n + 3n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-22 + -5n + 3n2 = 0

Factor a trinomial.
(-2 + -1n)(11 + -3n) = 0

Subproblem 1

Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2

Subproblem 2

Set the factor '(11 + -3n)' equal to zero and attempt to solve: Simplifying 11 + -3n = 0 Solving 11 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3n = 0 + -11 -3n = 0 + -11 Combine like terms: 0 + -11 = -11 -3n = -11 Divide each side by '-3'. n = 3.666666667 Simplifying n = 3.666666667

Solution

n = {-2, 3.666666667}

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