5n(2n+3)=2n+4(n-2)

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Solution for 5n(2n+3)=2n+4(n-2) equation: 


Simplifying
5n(2n + 3) = 2n + 4(n + -2)

Reorder the terms:
5n(3 + 2n) = 2n + 4(n + -2)
(3 * 5n + 2n * 5n) = 2n + 4(n + -2)
(15n + 10n2) = 2n + 4(n + -2)

Reorder the terms:
15n + 10n2 = 2n + 4(-2 + n)
15n + 10n2 = 2n + (-2 * 4 + n * 4)
15n + 10n2 = 2n + (-8 + 4n)

Reorder the terms:
15n + 10n2 = -8 + 2n + 4n

Combine like terms: 2n + 4n = 6n
15n + 10n2 = -8 + 6n

Solving
15n + 10n2 = -8 + 6n

Solving for variable 'n'.

Reorder the terms:
8 + 15n + -6n + 10n2 = -8 + 6n + 8 + -6n

Combine like terms: 15n + -6n = 9n
8 + 9n + 10n2 = -8 + 6n + 8 + -6n

Reorder the terms:
8 + 9n + 10n2 = -8 + 8 + 6n + -6n

Combine like terms: -8 + 8 = 0
8 + 9n + 10n2 = 0 + 6n + -6n
8 + 9n + 10n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
8 + 9n + 10n2 = 0

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

Divide each side by '10'.
0.8 + 0.9n + n2 = 0.0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 0.9n + -0.8 + n2 = 0.0 + -0.8

Reorder the terms:
0.8 + -0.8 + 0.9n + n2 = 0.0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 0.9n + n2 = 0.0 + -0.8
0.9n + n2 = 0.0 + -0.8

Combine like terms: 0.0 + -0.8 = -0.8
0.9n + n2 = -0.8

The n term is 0.9n.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9n + 0.2025 + n2 = -0.8 + 0.2025

Reorder the terms:
0.2025 + 0.9n + n2 = -0.8 + 0.2025

Combine like terms: -0.8 + 0.2025 = -0.5975
0.2025 + 0.9n + n2 = -0.5975

Factor a perfect square on the left side:
(n + 0.45)(n + 0.45) = -0.5975

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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