-3n(n+4)=6(1-n)

Solution for -3n(n+4)=6(1-n) equation:

Simplifying
-3n(n + 4) = 6(1 + -1n)

Reorder the terms:
-3n(4 + n) = 6(1 + -1n)
(4 * -3n + n * -3n) = 6(1 + -1n)
(-12n + -3n2) = 6(1 + -1n)
-12n + -3n2 = (1 * 6 + -1n * 6)
-12n + -3n2 = (6 + -6n)

Solving
-12n + -3n2 = 6 + -6n

Solving for variable 'n'.

Reorder the terms:
-6 + -12n + 6n + -3n2 = 6 + -6n + -6 + 6n

Combine like terms: -12n + 6n = -6n
-6 + -6n + -3n2 = 6 + -6n + -6 + 6n

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

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

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

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

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

Simplifying
2 + 2n + n2 = 0

Solving
2 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = -2 + 1

Reorder the terms:
1 + 2n + n2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2n + n2 = -1

Factor a perfect square on the left side:
(n + 1)(n + 1) = -1

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.