2n^2=9n-10

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Solution for 2n^2=9n-10 equation:


Simplifying
2n2 = 9n + -10

Reorder the terms:
2n2 = -10 + 9n

Solving
2n2 = -10 + 9n

Solving for variable 'n'.

Reorder the terms:
10 + -9n + 2n2 = -10 + 9n + 10 + -9n

Reorder the terms:
10 + -9n + 2n2 = -10 + 10 + 9n + -9n

Combine like terms: -10 + 10 = 0
10 + -9n + 2n2 = 0 + 9n + -9n
10 + -9n + 2n2 = 9n + -9n

Combine like terms: 9n + -9n = 0
10 + -9n + 2n2 = 0

Factor a trinomial.
(2 + -1n)(5 + -2n) = 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 '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5

Solution

n = {2, 2.5}

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