-10n-5(3-n)(2n+11)=-30n

Solution for -10n-5(3-n)(2n+11)=-30n equation:

Simplifying
-10n + -5(3 + -1n)(2n + 11) = -30n

Reorder the terms:
-10n + -5(3 + -1n)(11 + 2n) = -30n

Multiply (3 + -1n) * (11 + 2n)
-10n + -5(3(11 + 2n) + -1n * (11 + 2n)) = -30n
-10n + -5((11 * 3 + 2n * 3) + -1n * (11 + 2n)) = -30n
-10n + -5((33 + 6n) + -1n * (11 + 2n)) = -30n
-10n + -5(33 + 6n + (11 * -1n + 2n * -1n)) = -30n
-10n + -5(33 + 6n + (-11n + -2n2)) = -30n

Combine like terms: 6n + -11n = -5n
-10n + -5(33 + -5n + -2n2) = -30n
-10n + (33 * -5 + -5n * -5 + -2n2 * -5) = -30n
-10n + (-165 + 25n + 10n2) = -30n

Reorder the terms:
-165 + -10n + 25n + 10n2 = -30n

Combine like terms: -10n + 25n = 15n
-165 + 15n + 10n2 = -30n

Solving
-165 + 15n + 10n2 = -30n

Solving for variable 'n'.

Reorder the terms:
-165 + 15n + 30n + 10n2 = -30n + 30n

Combine like terms: 15n + 30n = 45n
-165 + 45n + 10n2 = -30n + 30n

Combine like terms: -30n + 30n = 0
-165 + 45n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-33 + 9n + 2n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-33 + 9n + 2n2)' equal to zero and attempt to solve:

Simplifying
-33 + 9n + 2n2 = 0

Solving
-33 + 9n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-16.5 + 4.5n + n2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 4.5n + 16.5 + n2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 4.5n + n2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 4.5n + n2 = 0 + 16.5
4.5n + n2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
4.5n + n2 = 16.5

The n term is 4.5n.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5n + 5.0625 + n2 = 16.5 + 5.0625

Reorder the terms:
5.0625 + 4.5n + n2 = 16.5 + 5.0625

Combine like terms: 16.5 + 5.0625 = 21.5625
5.0625 + 4.5n + n2 = 21.5625

Factor a perfect square on the left side:
(n + 2.25)(n + 2.25) = 21.5625

Calculate the square root of the right side: 4.643543905

Break this problem into two subproblems by setting 
(n + 2.25) equal to 4.643543905 and -4.643543905.

Subproblem 1
n + 2.25 = 4.643543905

Simplifying
n + 2.25 = 4.643543905

Reorder the terms:
2.25 + n = 4.643543905

Solving
2.25 + n = 4.643543905

Solving for variable 'n'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + n = 4.643543905 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + n = 4.643543905 + -2.25
n = 4.643543905 + -2.25

Combine like terms: 4.643543905 + -2.25 = 2.393543905
n = 2.393543905

Simplifying
n = 2.393543905

Subproblem 2
n + 2.25 = -4.643543905

Simplifying
n + 2.25 = -4.643543905

Reorder the terms:
2.25 + n = -4.643543905

Solving
2.25 + n = -4.643543905

Solving for variable 'n'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + n = -4.643543905 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + n = -4.643543905 + -2.25
n = -4.643543905 + -2.25

Combine like terms: -4.643543905 + -2.25 = -6.893543905
n = -6.893543905

Simplifying
n = -6.893543905

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.393543905, -6.893543905}
Solution
n = {2.393543905, -6.893543905}