-3n(1-n)=-6-6n

Solution for -3n(1-n)=-6-6n equation:

Simplifying
-3n(1 + -1n) = -6 + -6n
(1 * -3n + -1n * -3n) = -6 + -6n
(-3n + 3n2) = -6 + -6n

Solving
-3n + 3n2 = -6 + -6n

Solving for variable 'n'.

Reorder the terms:
6 + -3n + 6n + 3n2 = -6 + -6n + 6 + 6n

Combine like terms: -3n + 6n = 3n
6 + 3n + 3n2 = -6 + -6n + 6 + 6n

Reorder the terms:
6 + 3n + 3n2 = -6 + 6 + -6n + 6n

Combine like terms: -6 + 6 = 0
6 + 3n + 3n2 = 0 + -6n + 6n
6 + 3n + 3n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
6 + 3n + 3n2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + n + n2)' equal to zero and attempt to solve:

Simplifying
2 + n + n2 = 0

Solving
2 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n + n2 = 0 + -2
n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
n + n2 = -2

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 = -2 + 0.25

Reorder the terms:
0.25 + n + n2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + n + n2 = -1.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -1.75

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.