(n+20)(n+20)=n(n-5)+22

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Solution for (n+20)(n+20)=n(n-5)+22 equation: 


Simplifying
(n + 20)(n + 20) = n(n + -5) + 22

Reorder the terms:
(20 + n)(n + 20) = n(n + -5) + 22

Reorder the terms:
(20 + n)(20 + n) = n(n + -5) + 22

Multiply (20 + n) * (20 + n)
(20(20 + n) + n(20 + n)) = n(n + -5) + 22
((20 * 20 + n * 20) + n(20 + n)) = n(n + -5) + 22
((400 + 20n) + n(20 + n)) = n(n + -5) + 22
(400 + 20n + (20 * n + n * n)) = n(n + -5) + 22
(400 + 20n + (20n + n2)) = n(n + -5) + 22

Combine like terms: 20n + 20n = 40n
(400 + 40n + n2) = n(n + -5) + 22

Reorder the terms:
400 + 40n + n2 = n(-5 + n) + 22
400 + 40n + n2 = (-5 * n + n * n) + 22
400 + 40n + n2 = (-5n + n2) + 22

Reorder the terms:
400 + 40n + n2 = 22 + -5n + n2

Add '-1n2' to each side of the equation.
400 + 40n + n2 + -1n2 = 22 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
400 + 40n + 0 = 22 + -5n + n2 + -1n2
400 + 40n = 22 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
400 + 40n = 22 + -5n + 0
400 + 40n = 22 + -5n

Solving
400 + 40n = 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.
400 + 40n + 5n = 22 + -5n + 5n

Combine like terms: 40n + 5n = 45n
400 + 45n = 22 + -5n + 5n

Combine like terms: -5n + 5n = 0
400 + 45n = 22 + 0
400 + 45n = 22

Add '-400' to each side of the equation.
400 + -400 + 45n = 22 + -400

Combine like terms: 400 + -400 = 0
0 + 45n = 22 + -400
45n = 22 + -400

Combine like terms: 22 + -400 = -378
45n = -378

Divide each side by '45'.
n = -8.4

Simplifying
n = -8.4

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