6n-18=4n(n+2)

Solution for 6n-18=4n(n+2) equation:

Simplifying
6n + -18 = 4n(n + 2)

Reorder the terms:
-18 + 6n = 4n(n + 2)

Reorder the terms:
-18 + 6n = 4n(2 + n)
-18 + 6n = (2 * 4n + n * 4n)
-18 + 6n = (8n + 4n2)

Solving
-18 + 6n = 8n + 4n2

Solving for variable 'n'.

Combine like terms: 6n + -8n = -2n
-18 + -2n + -4n2 = 8n + 4n2 + -8n + -4n2

Reorder the terms:
-18 + -2n + -4n2 = 8n + -8n + 4n2 + -4n2

Combine like terms: 8n + -8n = 0
-18 + -2n + -4n2 = 0 + 4n2 + -4n2
-18 + -2n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-18 + -2n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(9 + n + 2n2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(9 + n + 2n2)' equal to zero and attempt to solve:

Simplifying
9 + n + 2n2 = 0

Solving
9 + n + 2n2 = 0

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

Divide each side by '2'.
4.5 + 0.5n + n2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 0.5n + -4.5 + n2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 0.5n + n2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 0.5n + n2 = 0 + -4.5
0.5n + n2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
0.5n + n2 = -4.5

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.
0.5n + 0.25 + n2 = -4.5 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = -4.5 + 0.25

Combine like terms: -4.5 + 0.25 = -4.25
0.25 + 0.5n + n2 = -4.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -4.25

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.