(10n+1)(10n+1)=

Solution for (10n+1)(10n+1)= equation:

Simplifying
(10n + 1)(10n + 1) = 0

Reorder the terms:
(1 + 10n)(10n + 1) = 0

Reorder the terms:
(1 + 10n)(1 + 10n) = 0

Multiply (1 + 10n) * (1 + 10n)
(1(1 + 10n) + 10n * (1 + 10n)) = 0
((1 * 1 + 10n * 1) + 10n * (1 + 10n)) = 0
((1 + 10n) + 10n * (1 + 10n)) = 0
(1 + 10n + (1 * 10n + 10n * 10n)) = 0
(1 + 10n + (10n + 100n2)) = 0

Combine like terms: 10n + 10n = 20n
(1 + 20n + 100n2) = 0

Solving
1 + 20n + 100n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + 10n)(1 + 10n) = 0

Subproblem 1
Set the factor '(1 + 10n)' equal to zero and attempt to solve:

Simplifying
1 + 10n = 0

Solving
1 + 10n = 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 + 10n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10n = 0 + -1
10n = 0 + -1

Combine like terms: 0 + -1 = -1
10n = -1

Divide each side by '10'.
n = -0.1

Simplifying
n = -0.1
Subproblem 2
Set the factor '(1 + 10n)' equal to zero and attempt to solve:

Simplifying
1 + 10n = 0

Solving
1 + 10n = 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 + 10n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10n = 0 + -1
10n = 0 + -1

Combine like terms: 0 + -1 = -1
10n = -1

Divide each side by '10'.
n = -0.1

Simplifying
n = -0.1
Solution
n = {-0.1, -0.1}