5n^2+36n+19=-n+5

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Solution for 5n^2+36n+19=-n+5 equation:


Simplifying
5n2 + 36n + 19 = -1n + 5

Reorder the terms:
19 + 36n + 5n2 = -1n + 5

Reorder the terms:
19 + 36n + 5n2 = 5 + -1n

Solving
19 + 36n + 5n2 = 5 + -1n

Solving for variable 'n'.

Reorder the terms:
19 + -5 + 36n + n + 5n2 = 5 + -1n + -5 + n

Combine like terms: 19 + -5 = 14
14 + 36n + n + 5n2 = 5 + -1n + -5 + n

Combine like terms: 36n + n = 37n
14 + 37n + 5n2 = 5 + -1n + -5 + n

Reorder the terms:
14 + 37n + 5n2 = 5 + -5 + -1n + n

Combine like terms: 5 + -5 = 0
14 + 37n + 5n2 = 0 + -1n + n
14 + 37n + 5n2 = -1n + n

Combine like terms: -1n + n = 0
14 + 37n + 5n2 = 0

Factor a trinomial.
(7 + n)(2 + 5n) = 0

Subproblem 1

Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7

Subproblem 2

Set the factor '(2 + 5n)' equal to zero and attempt to solve: Simplifying 2 + 5n = 0 Solving 2 + 5n = 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 + 5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5n = 0 + -2 5n = 0 + -2 Combine like terms: 0 + -2 = -2 5n = -2 Divide each side by '5'. n = -0.4 Simplifying n = -0.4

Solution

n = {-7, -0.4}

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