n^2=10+3n

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Solution for n^2=10+3n equation:


Simplifying
n2 = 10 + 3n

Solving
n2 = 10 + 3n

Solving for variable 'n'.

Reorder the terms:
-10 + -3n + n2 = 10 + 3n + -10 + -3n

Reorder the terms:
-10 + -3n + n2 = 10 + -10 + 3n + -3n

Combine like terms: 10 + -10 = 0
-10 + -3n + n2 = 0 + 3n + -3n
-10 + -3n + n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-10 + -3n + n2 = 0

Factor a trinomial.
(-2 + -1n)(5 + -1n) = 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 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5

Solution

n = {-2, 5}

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