9n^2+6n+1=49

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Solution for 9n^2+6n+1=49 equation:


Simplifying
9n2 + 6n + 1 = 49

Reorder the terms:
1 + 6n + 9n2 = 49

Solving
1 + 6n + 9n2 = 49

Solving for variable 'n'.

Reorder the terms:
1 + -49 + 6n + 9n2 = 49 + -49

Combine like terms: 1 + -49 = -48
-48 + 6n + 9n2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48 + 6n + 9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 2n + 3n2) = 0

Factor a trinomial.
3((-8 + -3n)(2 + -1n)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-8 + -3n)' equal to zero and attempt to solve: Simplifying -8 + -3n = 0 Solving -8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n = 0 + 8 -3n = 0 + 8 Combine like terms: 0 + 8 = 8 -3n = 8 Divide each side by '-3'. n = -2.666666667 Simplifying n = -2.666666667

Subproblem 2

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

Solution

n = {-2.666666667, 2}

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