28=-4n(n+15)

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Solution for 28=-4n(n+15) equation: 


Simplifying
28 = -4n(n + 15)

Reorder the terms:
28 = -4n(15 + n)
28 = (15 * -4n + n * -4n)
28 = (-60n + -4n2)

Solving
28 = -60n + -4n2

Solving for variable 'n'.

Reorder the terms:
28 + 60n + 4n2 = -60n + 60n + -4n2 + 4n2

Combine like terms: -60n + 60n = 0
28 + 60n + 4n2 = 0 + -4n2 + 4n2
28 + 60n + 4n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
28 + 60n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 15n + n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + 15n + n2)' equal to zero and attempt to solve:

Simplifying
7 + 15n + n2 = 0

Solving
7 + 15n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 15n + -7 + n2 = 0 + -7

Reorder the terms:
7 + -7 + 15n + n2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 15n + n2 = 0 + -7
15n + n2 = 0 + -7

Combine like terms: 0 + -7 = -7
15n + n2 = -7

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 = -7 + 56.25

Reorder the terms:
56.25 + 15n + n2 = -7 + 56.25

Combine like terms: -7 + 56.25 = 49.25
56.25 + 15n + n2 = 49.25

Factor a perfect square on the left side:
(n + 7.5)(n + 7.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(n + 7.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
n + 7.5 = 7.017834424

Simplifying
n + 7.5 = 7.017834424

Reorder the terms:
7.5 + n = 7.017834424

Solving
7.5 + n = 7.017834424

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + n = 7.017834424 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + n = 7.017834424 + -7.5
n = 7.017834424 + -7.5

Combine like terms: 7.017834424 + -7.5 = -0.482165576
n = -0.482165576

Simplifying
n = -0.482165576


Subproblem 2
n + 7.5 = -7.017834424

Simplifying
n + 7.5 = -7.017834424

Reorder the terms:
7.5 + n = -7.017834424

Solving
7.5 + n = -7.017834424

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + n = -7.017834424 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + n = -7.017834424 + -7.5
n = -7.017834424 + -7.5

Combine like terms: -7.017834424 + -7.5 = -14.517834424
n = -14.517834424

Simplifying
n = -14.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.482165576, -14.517834424}
Solution
n = {-0.482165576, -14.517834424}

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