5n^2-6n+9=4n^2

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Solution for 5n^2-6n+9=4n^2 equation:


Simplifying
5n2 + -6n + 9 = 4n2

Reorder the terms:
9 + -6n + 5n2 = 4n2

Solving
9 + -6n + 5n2 = 4n2

Solving for variable 'n'.

Combine like terms: 5n2 + -4n2 = 1n2
9 + -6n + 1n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
9 + -6n + 1n2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

n = {3, 3}

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