4n+8=n^2+6n+9

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Solution for 4n+8=n^2+6n+9 equation:


Simplifying
4n + 8 = n2 + 6n + 9

Reorder the terms:
8 + 4n = n2 + 6n + 9

Reorder the terms:
8 + 4n = 9 + 6n + n2

Solving
8 + 4n = 9 + 6n + n2

Solving for variable 'n'.

Reorder the terms:
8 + -9 + 4n + -6n + -1n2 = 9 + 6n + n2 + -9 + -6n + -1n2

Combine like terms: 8 + -9 = -1
-1 + 4n + -6n + -1n2 = 9 + 6n + n2 + -9 + -6n + -1n2

Combine like terms: 4n + -6n = -2n
-1 + -2n + -1n2 = 9 + 6n + n2 + -9 + -6n + -1n2

Reorder the terms:
-1 + -2n + -1n2 = 9 + -9 + 6n + -6n + n2 + -1n2

Combine like terms: 9 + -9 = 0
-1 + -2n + -1n2 = 0 + 6n + -6n + n2 + -1n2
-1 + -2n + -1n2 = 6n + -6n + n2 + -1n2

Combine like terms: 6n + -6n = 0
-1 + -2n + -1n2 = 0 + n2 + -1n2
-1 + -2n + -1n2 = n2 + -1n2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2n + n2) = 0

Factor a trinomial.
-1((1 + n)(1 + n)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1

Subproblem 2

Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1

Solution

n = {-1, -1}

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