-6n-20=-2n+4n(1-3n)

Solution for -6n-20=-2n+4n(1-3n) equation:

Simplifying
-6n + -20 = -2n + 4n(1 + -3n)

Reorder the terms:
-20 + -6n = -2n + 4n(1 + -3n)
-20 + -6n = -2n + (1 * 4n + -3n * 4n)
-20 + -6n = -2n + (4n + -12n2)

Combine like terms: -2n + 4n = 2n
-20 + -6n = 2n + -12n2

Solving
-20 + -6n = 2n + -12n2

Solving for variable 'n'.

Combine like terms: -6n + -2n = -8n
-20 + -8n + 12n2 = 2n + -12n2 + -2n + 12n2

Reorder the terms:
-20 + -8n + 12n2 = 2n + -2n + -12n2 + 12n2

Combine like terms: 2n + -2n = 0
-20 + -8n + 12n2 = 0 + -12n2 + 12n2
-20 + -8n + 12n2 = -12n2 + 12n2

Combine like terms: -12n2 + 12n2 = 0
-20 + -8n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -2n + 3n2) = 0

Factor a trinomial.
4((-1 + -1n)(5 + -3n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve:

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-1, 1.666666667}