-8(n+7)-4n(1-3n)=

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Solution for -8(n+7)-4n(1-3n)= equation: 


Simplifying
-8(n + 7) + -4n(1 + -3n) = 0

Reorder the terms:
-8(7 + n) + -4n(1 + -3n) = 0
(7 * -8 + n * -8) + -4n(1 + -3n) = 0
(-56 + -8n) + -4n(1 + -3n) = 0
-56 + -8n + (1 * -4n + -3n * -4n) = 0
-56 + -8n + (-4n + 12n2) = 0

Combine like terms: -8n + -4n = -12n
-56 + -12n + 12n2 = 0

Solving
-56 + -12n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -3n + 3n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + -3n + 3n2)' equal to zero and attempt to solve:

Simplifying
-14 + -3n + 3n2 = 0

Solving
-14 + -3n + 3n2 = 0

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

Divide each side by '3'.
-4.666666667 + -1n + n2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -1n + 4.666666667 + n2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -1n + n2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -1n + n2 = 0 + 4.666666667
-1n + n2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-1n + n2 = 4.666666667

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 = 4.666666667 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 4.666666667 + 0.25

Combine like terms: 4.666666667 + 0.25 = 4.916666667
0.25 + -1n + n2 = 4.916666667

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 4.916666667

Calculate the square root of the right side: 2.217355783

Break this problem into two subproblems by setting 
(n + -0.5) equal to 2.217355783 and -2.217355783.


Subproblem 1
n + -0.5 = 2.217355783

Simplifying
n + -0.5 = 2.217355783

Reorder the terms:
-0.5 + n = 2.217355783

Solving
-0.5 + n = 2.217355783

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 = 2.217355783 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 2.217355783 + 0.5
n = 2.217355783 + 0.5

Combine like terms: 2.217355783 + 0.5 = 2.717355783
n = 2.717355783

Simplifying
n = 2.717355783


Subproblem 2
n + -0.5 = -2.217355783

Simplifying
n + -0.5 = -2.217355783

Reorder the terms:
-0.5 + n = -2.217355783

Solving
-0.5 + n = -2.217355783

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 = -2.217355783 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -2.217355783 + 0.5
n = -2.217355783 + 0.5

Combine like terms: -2.217355783 + 0.5 = -1.717355783
n = -1.717355783

Simplifying
n = -1.717355783


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.717355783, -1.717355783}
Solution
n = {2.717355783, -1.717355783}

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