-n^2=3n+6

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Solution for -n^2=3n+6 equation:


Simplifying
-1n2 = 3n + 6

Reorder the terms:
-1n2 = 6 + 3n

Solving
-1n2 = 6 + 3n

Solving for variable 'n'.

Reorder the terms:
-6 + -3n + -1n2 = 6 + 3n + -6 + -3n

Reorder the terms:
-6 + -3n + -1n2 = 6 + -6 + 3n + -3n

Combine like terms: 6 + -6 = 0
-6 + -3n + -1n2 = 0 + 3n + -3n
-6 + -3n + -1n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-6 + -3n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 3n + n2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(6 + 3n + n2)' equal to zero and attempt to solve: Simplifying 6 + 3n + n2 = 0 Solving 6 + 3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 3n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3n + n2 = 0 + -6 3n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 3n + n2 = -6 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = -6 + 2.25 Reorder the terms: 2.25 + 3n + n2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + 3n + n2 = -3.75 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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