n(75-5n)=14400

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Solution for n(75-5n)=14400 equation: 


Simplifying
n(75 + -5n) = 14400
(75 * n + -5n * n) = 14400
(75n + -5n2) = 14400

Solving
75n + -5n2 = 14400

Solving for variable 'n'.

Reorder the terms:
-14400 + 75n + -5n2 = 14400 + -14400

Combine like terms: 14400 + -14400 = 0
-14400 + 75n + -5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2880 + 15n + -1n2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2880 + 15n + -1n2)' equal to zero and attempt to solve:

Simplifying
-2880 + 15n + -1n2 = 0

Solving
-2880 + 15n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2880 + -15n + n2 = 0

Move the constant term to the right:

Add '-2880' to each side of the equation.
2880 + -15n + -2880 + n2 = 0 + -2880

Reorder the terms:
2880 + -2880 + -15n + n2 = 0 + -2880

Combine like terms: 2880 + -2880 = 0
0 + -15n + n2 = 0 + -2880
-15n + n2 = 0 + -2880

Combine like terms: 0 + -2880 = -2880
-15n + n2 = -2880

The n term is -15n.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15n + 56.25 + n2 = -2880 + 56.25

Reorder the terms:
56.25 + -15n + n2 = -2880 + 56.25

Combine like terms: -2880 + 56.25 = -2823.75
56.25 + -15n + n2 = -2823.75

Factor a perfect square on the left side:
(n + -7.5)(n + -7.5) = -2823.75

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.

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