n(1-2n)+3n(1+n)=

Solution for n(1-2n)+3n(1+n)= equation:

Simplifying
n(1 + -2n) + 3n(1 + n) = 0
(1 * n + -2n * n) + 3n(1 + n) = 0
(1n + -2n2) + 3n(1 + n) = 0
1n + -2n2 + (1 * 3n + n * 3n) = 0
1n + -2n2 + (3n + 3n2) = 0

Reorder the terms:
1n + 3n + -2n2 + 3n2 = 0

Combine like terms: 1n + 3n = 4n
4n + -2n2 + 3n2 = 0

Combine like terms: -2n2 + 3n2 = 1n2
4n + 1n2 = 0

Solving
4n + 1n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(4 + n) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {0, -4}