(n+2)(n+2)=n(n-5)+22

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Solution for (n+2)(n+2)=n(n-5)+22 equation: 


Simplifying
(n + 2)(n + 2) = n(n + -5) + 22

Reorder the terms:
(2 + n)(n + 2) = n(n + -5) + 22

Reorder the terms:
(2 + n)(2 + n) = n(n + -5) + 22

Multiply (2 + n) * (2 + n)
(2(2 + n) + n(2 + n)) = n(n + -5) + 22
((2 * 2 + n * 2) + n(2 + n)) = n(n + -5) + 22
((4 + 2n) + n(2 + n)) = n(n + -5) + 22
(4 + 2n + (2 * n + n * n)) = n(n + -5) + 22
(4 + 2n + (2n + n2)) = n(n + -5) + 22

Combine like terms: 2n + 2n = 4n
(4 + 4n + n2) = n(n + -5) + 22

Reorder the terms:
4 + 4n + n2 = n(-5 + n) + 22
4 + 4n + n2 = (-5 * n + n * n) + 22
4 + 4n + n2 = (-5n + n2) + 22

Reorder the terms:
4 + 4n + n2 = 22 + -5n + n2

Add '-1n2' to each side of the equation.
4 + 4n + n2 + -1n2 = 22 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
4 + 4n + 0 = 22 + -5n + n2 + -1n2
4 + 4n = 22 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
4 + 4n = 22 + -5n + 0
4 + 4n = 22 + -5n

Solving
4 + 4n = 22 + -5n

Solving for variable 'n'.

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

Add '5n' to each side of the equation.
4 + 4n + 5n = 22 + -5n + 5n

Combine like terms: 4n + 5n = 9n
4 + 9n = 22 + -5n + 5n

Combine like terms: -5n + 5n = 0
4 + 9n = 22 + 0
4 + 9n = 22

Add '-4' to each side of the equation.
4 + -4 + 9n = 22 + -4

Combine like terms: 4 + -4 = 0
0 + 9n = 22 + -4
9n = 22 + -4

Combine like terms: 22 + -4 = 18
9n = 18

Divide each side by '9'.
n = 2

Simplifying
n = 2

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