n^2=7n-10

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Solution for n^2=7n-10 equation:


Simplifying
n2 = 7n + -10

Reorder the terms:
n2 = -10 + 7n

Solving
n2 = -10 + 7n

Solving for variable 'n'.

Reorder the terms:
10 + -7n + n2 = -10 + 7n + 10 + -7n

Reorder the terms:
10 + -7n + n2 = -10 + 10 + 7n + -7n

Combine like terms: -10 + 10 = 0
10 + -7n + n2 = 0 + 7n + -7n
10 + -7n + n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
10 + -7n + 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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