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

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

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

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

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

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

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

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

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

Solving for variable 'n'.

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

Combine like terms: -165 + 30 = -135
-135 + 15n + 10n2 = -30 + 30

Combine like terms: -30 + 30 = 0
-135 + 15n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-27 + 3n + 2n2) = 0

Factor a trinomial.
5((-9 + -2n)(3 + -1n)) = 0

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

Simplifying
-9 + -2n = 0

Solving
-9 + -2n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2n = 0 + 9
-2n = 0 + 9

Combine like terms: 0 + 9 = 9
-2n = 9

Divide each side by '-2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4.5, 3}