(n+5)(n+5)-(n+3)(n+3)=4(n+4)

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Solution for (n+5)(n+5)-(n+3)(n+3)=4(n+4) equation: 


Simplifying
(n + 5)(n + 5) + -1(n + 3)(n + 3) = 4(n + 4)

Reorder the terms:
(5 + n)(n + 5) + -1(n + 3)(n + 3) = 4(n + 4)

Reorder the terms:
(5 + n)(5 + n) + -1(n + 3)(n + 3) = 4(n + 4)

Multiply (5 + n) * (5 + n)
(5(5 + n) + n(5 + n)) + -1(n + 3)(n + 3) = 4(n + 4)
((5 * 5 + n * 5) + n(5 + n)) + -1(n + 3)(n + 3) = 4(n + 4)
((25 + 5n) + n(5 + n)) + -1(n + 3)(n + 3) = 4(n + 4)
(25 + 5n + (5 * n + n * n)) + -1(n + 3)(n + 3) = 4(n + 4)
(25 + 5n + (5n + n2)) + -1(n + 3)(n + 3) = 4(n + 4)

Combine like terms: 5n + 5n = 10n
(25 + 10n + n2) + -1(n + 3)(n + 3) = 4(n + 4)

Reorder the terms:
25 + 10n + n2 + -1(3 + n)(n + 3) = 4(n + 4)

Reorder the terms:
25 + 10n + n2 + -1(3 + n)(3 + n) = 4(n + 4)

Multiply (3 + n) * (3 + n)
25 + 10n + n2 + -1(3(3 + n) + n(3 + n)) = 4(n + 4)
25 + 10n + n2 + -1((3 * 3 + n * 3) + n(3 + n)) = 4(n + 4)
25 + 10n + n2 + -1((9 + 3n) + n(3 + n)) = 4(n + 4)
25 + 10n + n2 + -1(9 + 3n + (3 * n + n * n)) = 4(n + 4)
25 + 10n + n2 + -1(9 + 3n + (3n + n2)) = 4(n + 4)

Combine like terms: 3n + 3n = 6n
25 + 10n + n2 + -1(9 + 6n + n2) = 4(n + 4)
25 + 10n + n2 + (9 * -1 + 6n * -1 + n2 * -1) = 4(n + 4)
25 + 10n + n2 + (-9 + -6n + -1n2) = 4(n + 4)

Reorder the terms:
25 + -9 + 10n + -6n + n2 + -1n2 = 4(n + 4)

Combine like terms: 25 + -9 = 16
16 + 10n + -6n + n2 + -1n2 = 4(n + 4)

Combine like terms: 10n + -6n = 4n
16 + 4n + n2 + -1n2 = 4(n + 4)

Combine like terms: n2 + -1n2 = 0
16 + 4n + 0 = 4(n + 4)
16 + 4n = 4(n + 4)

Reorder the terms:
16 + 4n = 4(4 + n)
16 + 4n = (4 * 4 + n * 4)
16 + 4n = (16 + 4n)

Add '-16' to each side of the equation.
16 + -16 + 4n = 16 + -16 + 4n

Combine like terms: 16 + -16 = 0
0 + 4n = 16 + -16 + 4n
4n = 16 + -16 + 4n

Combine like terms: 16 + -16 = 0
4n = 0 + 4n
4n = 4n

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

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

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

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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