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

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


Simplifying
3n(n + -3) + 4(n + 4) = 0

Reorder the terms:
3n(-3 + n) + 4(n + 4) = 0
(-3 * 3n + n * 3n) + 4(n + 4) = 0
(-9n + 3n2) + 4(n + 4) = 0

Reorder the terms:
-9n + 3n2 + 4(4 + n) = 0
-9n + 3n2 + (4 * 4 + n * 4) = 0
-9n + 3n2 + (16 + 4n) = 0

Reorder the terms:
16 + -9n + 4n + 3n2 = 0

Combine like terms: -9n + 4n = -5n
16 + -5n + 3n2 = 0

Solving
16 + -5n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
5.333333333 + -1.666666667n + n2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -1.666666667n + -5.333333333 + n2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -1.666666667n + n2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -1.666666667n + n2 = 0 + -5.333333333
-1.666666667n + n2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-1.666666667n + n2 = -5.333333333

The n term is -1.666666667n.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667n + 0.6944444447 + n2 = -5.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667n + n2 = -5.333333333 + 0.6944444447

Combine like terms: -5.333333333 + 0.6944444447 = -4.6388888883
0.6944444447 + -1.666666667n + n2 = -4.6388888883

Factor a perfect square on the left side:
(n + -0.8333333335)(n + -0.8333333335) = -4.6388888883

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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