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

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

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

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

Multiply -10 * 2
-20n + -5(3 + -1n)(2n + 11) = -30

Reorder the terms:
-20n + -5(3 + -1n)(11 + 2n) = -30

Multiply (3 + -1n) * (11 + 2n)
-20n + -5(3(11 + 2n) + -1n * (11 + 2n)) = -30
-20n + -5((11 * 3 + 2n * 3) + -1n * (11 + 2n)) = -30
-20n + -5((33 + 6n) + -1n * (11 + 2n)) = -30
-20n + -5(33 + 6n + (11 * -1n + 2n * -1n)) = -30
-20n + -5(33 + 6n + (-11n + -2n2)) = -30

Combine like terms: 6n + -11n = -5n
-20n + -5(33 + -5n + -2n2) = -30
-20n + (33 * -5 + -5n * -5 + -2n2 * -5) = -30
-20n + (-165 + 25n + 10n2) = -30

Reorder the terms:
-165 + -20n + 25n + 10n2 = -30

Combine like terms: -20n + 25n = 5n
-165 + 5n + 10n2 = -30

Solving
-165 + 5n + 10n2 = -30

Solving for variable 'n'.

Reorder the terms:
-165 + 30 + 5n + 10n2 = -30 + 30

Combine like terms: -165 + 30 = -135
-135 + 5n + 10n2 = -30 + 30

Combine like terms: -30 + 30 = 0
-135 + 5n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-27 + n + 2n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-27 + n + 2n2)' equal to zero and attempt to solve:

Simplifying
-27 + n + 2n2 = 0

Solving
-27 + n + 2n2 = 0

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

Divide each side by '2'.
-13.5 + 0.5n + n2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 0.5n + 13.5 + n2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 0.5n + n2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 0.5n + n2 = 0 + 13.5
0.5n + n2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
0.5n + n2 = 13.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5n + 0.25 + n2 = 13.5 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = 13.5 + 0.25

Combine like terms: 13.5 + 0.25 = 13.75
0.25 + 0.5n + n2 = 13.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(n + 0.5) equal to 3.708099244 and -3.708099244.

Subproblem 1
n + 0.5 = 3.708099244

Simplifying
n + 0.5 = 3.708099244

Reorder the terms:
0.5 + n = 3.708099244

Solving
0.5 + n = 3.708099244

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 3.708099244 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 3.708099244 + -0.5
n = 3.708099244 + -0.5

Combine like terms: 3.708099244 + -0.5 = 3.208099244
n = 3.208099244

Simplifying
n = 3.208099244

Subproblem 2
n + 0.5 = -3.708099244

Simplifying
n + 0.5 = -3.708099244

Reorder the terms:
0.5 + n = -3.708099244

Solving
0.5 + n = -3.708099244

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -3.708099244 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -3.708099244 + -0.5
n = -3.708099244 + -0.5

Combine like terms: -3.708099244 + -0.5 = -4.208099244
n = -4.208099244

Simplifying
n = -4.208099244

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.208099244, -4.208099244}
Solution
n = {3.208099244, -4.208099244}