2n^2-21n+23=-n^2-7

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Solution for 2n^2-21n+23=-n^2-7 equation: 


Simplifying
2n2 + -21n + 23 = -1n2 + -7

Reorder the terms:
23 + -21n + 2n2 = -1n2 + -7

Reorder the terms:
23 + -21n + 2n2 = -7 + -1n2

Solving
23 + -21n + 2n2 = -7 + -1n2

Solving for variable 'n'.

Reorder the terms:
23 + 7 + -21n + 2n2 + n2 = -7 + -1n2 + 7 + n2

Combine like terms: 23 + 7 = 30
30 + -21n + 2n2 + n2 = -7 + -1n2 + 7 + n2

Combine like terms: 2n2 + n2 = 3n2
30 + -21n + 3n2 = -7 + -1n2 + 7 + n2

Reorder the terms:
30 + -21n + 3n2 = -7 + 7 + -1n2 + n2

Combine like terms: -7 + 7 = 0
30 + -21n + 3n2 = 0 + -1n2 + n2
30 + -21n + 3n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
30 + -21n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -7n + n2) = 0

Factor a trinomial.
3((2 + -1n)(5 + -1n)) = 0

Ignore the factor 3.

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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