30=-5n[6n+6]

Solution for 30=-5n[6n+6] equation:

Simplifying
30 = -5n[6n + 6]

Reorder the terms:
30 = -5n[6 + 6n]
30 = [6 * -5n + 6n * -5n]
30 = [-30n + -30n2]

Solving
30 = -30n + -30n2

Solving for variable 'n'.

Reorder the terms:
30 + 30n + 30n2 = -30n + 30n + -30n2 + 30n2

Combine like terms: -30n + 30n = 0
30 + 30n + 30n2 = 0 + -30n2 + 30n2
30 + 30n + 30n2 = -30n2 + 30n2

Combine like terms: -30n2 + 30n2 = 0
30 + 30n + 30n2 = 0

Factor out the Greatest Common Factor (GCF), '30'.
30(1 + n + n2) = 0

Ignore the factor 30.
Subproblem 1
Set the factor '(1 + n + n2)' equal to zero and attempt to solve:

Simplifying
1 + n + n2 = 0

Solving
1 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n + n2 = 0 + -1
n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
n + n2 = -1

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.
n + 0.25 + n2 = -1 + 0.25

Reorder the terms:
0.25 + n + n2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + n + n2 = -0.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.