(n^2+2n-9)-(n^2-3n+16)=n-5

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Solution for (n^2+2n-9)-(n^2-3n+16)=n-5 equation:


Simplifying
(n2 + 2n + -9) + -1(n2 + -3n + 16) = n + -5

Reorder the terms:
(-9 + 2n + n2) + -1(n2 + -3n + 16) = n + -5

Remove parenthesis around (-9 + 2n + n2)
-9 + 2n + n2 + -1(n2 + -3n + 16) = n + -5

Reorder the terms:
-9 + 2n + n2 + -1(16 + -3n + n2) = n + -5
-9 + 2n + n2 + (16 * -1 + -3n * -1 + n2 * -1) = n + -5
-9 + 2n + n2 + (-16 + 3n + -1n2) = n + -5

Reorder the terms:
-9 + -16 + 2n + 3n + n2 + -1n2 = n + -5

Combine like terms: -9 + -16 = -25
-25 + 2n + 3n + n2 + -1n2 = n + -5

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

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

Reorder the terms:
-25 + 5n = -5 + n

Solving
-25 + 5n = -5 + n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1n' to each side of the equation.
-25 + 5n + -1n = -5 + n + -1n

Combine like terms: 5n + -1n = 4n
-25 + 4n = -5 + n + -1n

Combine like terms: n + -1n = 0
-25 + 4n = -5 + 0
-25 + 4n = -5

Add '25' to each side of the equation.
-25 + 25 + 4n = -5 + 25

Combine like terms: -25 + 25 = 0
0 + 4n = -5 + 25
4n = -5 + 25

Combine like terms: -5 + 25 = 20
4n = 20

Divide each side by '4'.
n = 5

Simplifying
n = 5

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