5n(n+2)=6(2n-3)

Solution for 5n(n+2)=6(2n-3) equation:

Simplifying
5n(n + 2) = 6(2n + -3)

Reorder the terms:
5n(2 + n) = 6(2n + -3)
(2 * 5n + n * 5n) = 6(2n + -3)
(10n + 5n2) = 6(2n + -3)

Reorder the terms:
10n + 5n2 = 6(-3 + 2n)
10n + 5n2 = (-3 * 6 + 2n * 6)
10n + 5n2 = (-18 + 12n)

Solving
10n + 5n2 = -18 + 12n

Solving for variable 'n'.

Reorder the terms:
18 + 10n + -12n + 5n2 = -18 + 12n + 18 + -12n

Combine like terms: 10n + -12n = -2n
18 + -2n + 5n2 = -18 + 12n + 18 + -12n

Reorder the terms:
18 + -2n + 5n2 = -18 + 18 + 12n + -12n

Combine like terms: -18 + 18 = 0
18 + -2n + 5n2 = 0 + 12n + -12n
18 + -2n + 5n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
18 + -2n + 5n2 = 0

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

Divide each side by '5'.
3.6 + -0.4n + n2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + -0.4n + -3.6 + n2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + -0.4n + n2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + -0.4n + n2 = 0 + -3.6
-0.4n + n2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
-0.4n + n2 = -3.6

The n term is -0.4n.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4n + 0.04 + n2 = -3.6 + 0.04

Reorder the terms:
0.04 + -0.4n + n2 = -3.6 + 0.04

Combine like terms: -3.6 + 0.04 = -3.56
0.04 + -0.4n + n2 = -3.56

Factor a perfect square on the left side:
(n + -0.2)(n + -0.2) = -3.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.