0=n^2-9n+14

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Solution for 0=n^2-9n+14 equation:


Simplifying
0 = n2 + -9n + 14

Reorder the terms:
0 = 14 + -9n + n2

Solving
0 = 14 + -9n + n2

Solving for variable 'n'.

Combine like terms: 0 + -14 = -14
-14 + 9n + -1n2 = 14 + -9n + n2 + -14 + 9n + -1n2

Reorder the terms:
-14 + 9n + -1n2 = 14 + -14 + -9n + 9n + n2 + -1n2

Combine like terms: 14 + -14 = 0
-14 + 9n + -1n2 = 0 + -9n + 9n + n2 + -1n2
-14 + 9n + -1n2 = -9n + 9n + n2 + -1n2

Combine like terms: -9n + 9n = 0
-14 + 9n + -1n2 = 0 + n2 + -1n2
-14 + 9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-14 + 9n + -1n2 = 0

Factor a trinomial.
(-7 + n)(2 + -1n) = 0

Subproblem 1

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

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 = {7, 2}

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