-77=n(3-3n)

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Solution for -77=n(3-3n) equation: 


Simplifying
-77 = n(3 + -3n)
-77 = (3 * n + -3n * n)
-77 = (3n + -3n2)

Solving
-77 = 3n + -3n2

Solving for variable 'n'.

Reorder the terms:
-77 + -3n + 3n2 = 3n + -3n + -3n2 + 3n2

Combine like terms: 3n + -3n = 0
-77 + -3n + 3n2 = 0 + -3n2 + 3n2
-77 + -3n + 3n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-77 + -3n + 3n2 = 0

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

Divide each side by '3'.
-25.66666667 + -1n + n2 = 0

Move the constant term to the right:

Add '25.66666667' to each side of the equation.
-25.66666667 + -1n + 25.66666667 + n2 = 0 + 25.66666667

Reorder the terms:
-25.66666667 + 25.66666667 + -1n + n2 = 0 + 25.66666667

Combine like terms: -25.66666667 + 25.66666667 = 0.00000000
0.00000000 + -1n + n2 = 0 + 25.66666667
-1n + n2 = 0 + 25.66666667

Combine like terms: 0 + 25.66666667 = 25.66666667
-1n + n2 = 25.66666667

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 25.66666667 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 25.66666667 + 0.25

Combine like terms: 25.66666667 + 0.25 = 25.91666667
0.25 + -1n + n2 = 25.91666667

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 25.91666667

Calculate the square root of the right side: 5.09084145

Break this problem into two subproblems by setting 
(n + -0.5) equal to 5.09084145 and -5.09084145.


Subproblem 1
n + -0.5 = 5.09084145

Simplifying
n + -0.5 = 5.09084145

Reorder the terms:
-0.5 + n = 5.09084145

Solving
-0.5 + n = 5.09084145

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 5.09084145 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 5.09084145 + 0.5
n = 5.09084145 + 0.5

Combine like terms: 5.09084145 + 0.5 = 5.59084145
n = 5.59084145

Simplifying
n = 5.59084145


Subproblem 2
n + -0.5 = -5.09084145

Simplifying
n + -0.5 = -5.09084145

Reorder the terms:
-0.5 + n = -5.09084145

Solving
-0.5 + n = -5.09084145

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -5.09084145 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -5.09084145 + 0.5
n = -5.09084145 + 0.5

Combine like terms: -5.09084145 + 0.5 = -4.59084145
n = -4.59084145

Simplifying
n = -4.59084145


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.59084145, -4.59084145}

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