n-6(3n+1)=3n(n-5)

Solution for n-6(3n+1)=3n(n-5) equation:

Simplifying
n + -6(3n + 1) = 3n(n + -5)

Reorder the terms:
n + -6(1 + 3n) = 3n(n + -5)
n + (1 * -6 + 3n * -6) = 3n(n + -5)
n + (-6 + -18n) = 3n(n + -5)

Reorder the terms:
-6 + n + -18n = 3n(n + -5)

Combine like terms: n + -18n = -17n
-6 + -17n = 3n(n + -5)

Reorder the terms:
-6 + -17n = 3n(-5 + n)
-6 + -17n = (-5 * 3n + n * 3n)
-6 + -17n = (-15n + 3n2)

Solving
-6 + -17n = -15n + 3n2

Solving for variable 'n'.

Combine like terms: -17n + 15n = -2n
-6 + -2n + -3n2 = -15n + 3n2 + 15n + -3n2

Reorder the terms:
-6 + -2n + -3n2 = -15n + 15n + 3n2 + -3n2

Combine like terms: -15n + 15n = 0
-6 + -2n + -3n2 = 0 + 3n2 + -3n2
-6 + -2n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-6 + -2n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 2n + 3n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 2n + 3n2)' equal to zero and attempt to solve:

Simplifying
6 + 2n + 3n2 = 0

Solving
6 + 2n + 3n2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + 0.6666666667n + n2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.6666666667n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 0.6666666667n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.6666666667n + n2 = 0 + -2
0.6666666667n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.6666666667n + n2 = -2

The n term is 0.6666666667n.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667n + 0.1111111112 + n2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667n + n2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + 0.6666666667n + n2 = -1.8888888888

Factor a perfect square on the left side:
(n + 0.3333333334)(n + 0.3333333334) = -1.8888888888

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.