3n^2+10n+30=2n^2+5

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Solution for 3n^2+10n+30=2n^2+5 equation:


Simplifying
3n2 + 10n + 30 = 2n2 + 5

Reorder the terms:
30 + 10n + 3n2 = 2n2 + 5

Reorder the terms:
30 + 10n + 3n2 = 5 + 2n2

Solving
30 + 10n + 3n2 = 5 + 2n2

Solving for variable 'n'.

Reorder the terms:
30 + -5 + 10n + 3n2 + -2n2 = 5 + 2n2 + -5 + -2n2

Combine like terms: 30 + -5 = 25
25 + 10n + 3n2 + -2n2 = 5 + 2n2 + -5 + -2n2

Combine like terms: 3n2 + -2n2 = 1n2
25 + 10n + 1n2 = 5 + 2n2 + -5 + -2n2

Reorder the terms:
25 + 10n + 1n2 = 5 + -5 + 2n2 + -2n2

Combine like terms: 5 + -5 = 0
25 + 10n + 1n2 = 0 + 2n2 + -2n2
25 + 10n + 1n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
25 + 10n + 1n2 = 0

Factor a trinomial.
(5 + n)(5 + n) = 0

Subproblem 1

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Solution

n = {-5, -5}

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