5n(6-11n)-3(7n+8)=

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Solution for 5n(6-11n)-3(7n+8)= equation: 


Simplifying
5n(6 + -11n) + -3(7n + 8) = 0
(6 * 5n + -11n * 5n) + -3(7n + 8) = 0
(30n + -55n2) + -3(7n + 8) = 0

Reorder the terms:
30n + -55n2 + -3(8 + 7n) = 0
30n + -55n2 + (8 * -3 + 7n * -3) = 0
30n + -55n2 + (-24 + -21n) = 0

Reorder the terms:
-24 + 30n + -21n + -55n2 = 0

Combine like terms: 30n + -21n = 9n
-24 + 9n + -55n2 = 0

Solving
-24 + 9n + -55n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-55 the coefficient of the squared term: 

Divide each side by '-55'.
0.4363636364 + -0.1636363636n + n2 = 0

Move the constant term to the right:

Add '-0.4363636364' to each side of the equation.
0.4363636364 + -0.1636363636n + -0.4363636364 + n2 = 0 + -0.4363636364

Reorder the terms:
0.4363636364 + -0.4363636364 + -0.1636363636n + n2 = 0 + -0.4363636364

Combine like terms: 0.4363636364 + -0.4363636364 = 0.0000000000
0.0000000000 + -0.1636363636n + n2 = 0 + -0.4363636364
-0.1636363636n + n2 = 0 + -0.4363636364

Combine like terms: 0 + -0.4363636364 = -0.4363636364
-0.1636363636n + n2 = -0.4363636364

The n term is -0.1636363636n.  Take half its coefficient (-0.0818181818).
Square it (0.006694214873) and add it to both sides.

Add '0.006694214873' to each side of the equation.
-0.1636363636n + 0.006694214873 + n2 = -0.4363636364 + 0.006694214873

Reorder the terms:
0.006694214873 + -0.1636363636n + n2 = -0.4363636364 + 0.006694214873

Combine like terms: -0.4363636364 + 0.006694214873 = -0.429669421527
0.006694214873 + -0.1636363636n + n2 = -0.429669421527

Factor a perfect square on the left side:
(n + -0.0818181818)(n + -0.0818181818) = -0.429669421527

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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