101-n=(n+9)(n+9)

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Solution for 101-n=(n+9)(n+9) equation: 


Simplifying
101 + -1n = (n + 9)(n + 9)

Reorder the terms:
101 + -1n = (9 + n)(n + 9)

Reorder the terms:
101 + -1n = (9 + n)(9 + n)

Multiply (9 + n) * (9 + n)
101 + -1n = (9(9 + n) + n(9 + n))
101 + -1n = ((9 * 9 + n * 9) + n(9 + n))
101 + -1n = ((81 + 9n) + n(9 + n))
101 + -1n = (81 + 9n + (9 * n + n * n))
101 + -1n = (81 + 9n + (9n + n2))

Combine like terms: 9n + 9n = 18n
101 + -1n = (81 + 18n + n2)

Solving
101 + -1n = 81 + 18n + n2

Solving for variable 'n'.

Reorder the terms:
101 + -81 + -1n + -18n + -1n2 = 81 + 18n + n2 + -81 + -18n + -1n2

Combine like terms: 101 + -81 = 20
20 + -1n + -18n + -1n2 = 81 + 18n + n2 + -81 + -18n + -1n2

Combine like terms: -1n + -18n = -19n
20 + -19n + -1n2 = 81 + 18n + n2 + -81 + -18n + -1n2

Reorder the terms:
20 + -19n + -1n2 = 81 + -81 + 18n + -18n + n2 + -1n2

Combine like terms: 81 + -81 = 0
20 + -19n + -1n2 = 0 + 18n + -18n + n2 + -1n2
20 + -19n + -1n2 = 18n + -18n + n2 + -1n2

Combine like terms: 18n + -18n = 0
20 + -19n + -1n2 = 0 + n2 + -1n2
20 + -19n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
20 + -19n + -1n2 = 0

Factor a trinomial.
(1 + -1n)(20 + n) = 0


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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1

Subproblem 2
Set the factor '(20 + n)' equal to zero and attempt to solve:

Simplifying
20 + n = 0

Solving
20 + n = 0

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

Add '-20' to each side of the equation.
20 + -20 + n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + n = 0 + -20
n = 0 + -20

Combine like terms: 0 + -20 = -20
n = -20

Simplifying
n = -20
Solution
n = {1, -20}

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