(9n+9)(10n-2)=

Solution for (9n+9)(10n-2)= equation:

Simplifying
(9n + 9)(10n + -2) = 0

Reorder the terms:
(9 + 9n)(10n + -2) = 0

Reorder the terms:
(9 + 9n)(-2 + 10n) = 0

Multiply (9 + 9n) * (-2 + 10n)
(9(-2 + 10n) + 9n * (-2 + 10n)) = 0
((-2 * 9 + 10n * 9) + 9n * (-2 + 10n)) = 0
((-18 + 90n) + 9n * (-2 + 10n)) = 0
(-18 + 90n + (-2 * 9n + 10n * 9n)) = 0
(-18 + 90n + (-18n + 90n2)) = 0

Combine like terms: 90n + -18n = 72n
(-18 + 72n + 90n2) = 0

Solving
-18 + 72n + 90n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-1 + 4n + 5n2) = 0

Factor a trinomial.
18((-1 + -1n)(1 + -5n)) = 0

Ignore the factor 18.
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 '(1 + -5n)' equal to zero and attempt to solve:

Simplifying
1 + -5n = 0

Solving
1 + -5n = 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 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-1, 0.2}