39-8n=-8n(3+4n)+3n

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Solution for 39-8n=-8n(3+4n)+3n equation: 


Simplifying
39 + -8n = -8n(3 + 4n) + 3n
39 + -8n = (3 * -8n + 4n * -8n) + 3n
39 + -8n = (-24n + -32n2) + 3n

Reorder the terms:
39 + -8n = -24n + 3n + -32n2

Combine like terms: -24n + 3n = -21n
39 + -8n = -21n + -32n2

Solving
39 + -8n = -21n + -32n2

Solving for variable 'n'.

Combine like terms: -8n + 21n = 13n
39 + 13n + 32n2 = -21n + -32n2 + 21n + 32n2

Reorder the terms:
39 + 13n + 32n2 = -21n + 21n + -32n2 + 32n2

Combine like terms: -21n + 21n = 0
39 + 13n + 32n2 = 0 + -32n2 + 32n2
39 + 13n + 32n2 = -32n2 + 32n2

Combine like terms: -32n2 + 32n2 = 0
39 + 13n + 32n2 = 0

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

Divide each side by '32'.
1.21875 + 0.40625n + n2 = 0

Move the constant term to the right:

Add '-1.21875' to each side of the equation.
1.21875 + 0.40625n + -1.21875 + n2 = 0 + -1.21875

Reorder the terms:
1.21875 + -1.21875 + 0.40625n + n2 = 0 + -1.21875

Combine like terms: 1.21875 + -1.21875 = 0.00000
0.00000 + 0.40625n + n2 = 0 + -1.21875
0.40625n + n2 = 0 + -1.21875

Combine like terms: 0 + -1.21875 = -1.21875
0.40625n + n2 = -1.21875

The n term is 0.40625n.  Take half its coefficient (0.203125).
Square it (0.04125976563) and add it to both sides.

Add '0.04125976563' to each side of the equation.
0.40625n + 0.04125976563 + n2 = -1.21875 + 0.04125976563

Reorder the terms:
0.04125976563 + 0.40625n + n2 = -1.21875 + 0.04125976563

Combine like terms: -1.21875 + 0.04125976563 = -1.17749023437
0.04125976563 + 0.40625n + n2 = -1.17749023437

Factor a perfect square on the left side:
(n + 0.203125)(n + 0.203125) = -1.17749023437

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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