(n+15)*(n+15)=576

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Solution for (n+15)*(n+15)=576 equation: 


Simplifying
(n + 15)(n + 15) = 576

Reorder the terms:
(15 + n)(n + 15) = 576

Reorder the terms:
(15 + n)(15 + n) = 576

Multiply (15 + n) * (15 + n)
(15(15 + n) + n(15 + n)) = 576
((15 * 15 + n * 15) + n(15 + n)) = 576
((225 + 15n) + n(15 + n)) = 576
(225 + 15n + (15 * n + n * n)) = 576
(225 + 15n + (15n + n2)) = 576

Combine like terms: 15n + 15n = 30n
(225 + 30n + n2) = 576

Solving
225 + 30n + n2 = 576

Solving for variable 'n'.

Reorder the terms:
225 + -576 + 30n + n2 = 576 + -576

Combine like terms: 225 + -576 = -351
-351 + 30n + n2 = 576 + -576

Combine like terms: 576 + -576 = 0
-351 + 30n + n2 = 0

Factor a trinomial.
(-39 + -1n)(9 + -1n) = 0


Subproblem 1
Set the factor '(-39 + -1n)' equal to zero and attempt to solve:

Simplifying
-39 + -1n = 0

Solving
-39 + -1n = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1n = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1n = 0 + 39
-1n = 0 + 39

Combine like terms: 0 + 39 = 39
-1n = 39

Divide each side by '-1'.
n = -39

Simplifying
n = -39

Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-39, 9}

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