4n-9=2n(5+2n)

Solution for 4n-9=2n(5+2n) equation:

Simplifying
4n + -9 = 2n(5 + 2n)

Reorder the terms:
-9 + 4n = 2n(5 + 2n)
-9 + 4n = (5 * 2n + 2n * 2n)
-9 + 4n = (10n + 4n2)

Solving
-9 + 4n = 10n + 4n2

Solving for variable 'n'.

Combine like terms: 4n + -10n = -6n
-9 + -6n + -4n2 = 10n + 4n2 + -10n + -4n2

Reorder the terms:
-9 + -6n + -4n2 = 10n + -10n + 4n2 + -4n2

Combine like terms: 10n + -10n = 0
-9 + -6n + -4n2 = 0 + 4n2 + -4n2
-9 + -6n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-9 + -6n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 6n + 4n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + 6n + 4n2)' equal to zero and attempt to solve:

Simplifying
9 + 6n + 4n2 = 0

Solving
9 + 6n + 4n2 = 0

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

Divide each side by '4'.
2.25 + 1.5n + n2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 1.5n + -2.25 + n2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 1.5n + n2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 1.5n + n2 = 0 + -2.25
1.5n + n2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
1.5n + n2 = -2.25

The n term is 1.5n.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5n + 0.5625 + n2 = -2.25 + 0.5625

Reorder the terms:
0.5625 + 1.5n + n2 = -2.25 + 0.5625

Combine like terms: -2.25 + 0.5625 = -1.6875
0.5625 + 1.5n + n2 = -1.6875

Factor a perfect square on the left side:
(n + 0.75)(n + 0.75) = -1.6875

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.