3n^2+2n-1980=0

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Solution for 3n^2+2n-1980=0 equation: 


Simplifying
3n2 + 2n + -1980 = 0

Reorder the terms:
-1980 + 2n + 3n2 = 0

Solving
-1980 + 2n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-660 + 0.6666666667n + n2 = 0

Move the constant term to the right:

Add '660' to each side of the equation.
-660 + 0.6666666667n + 660 + n2 = 0 + 660

Reorder the terms:
-660 + 660 + 0.6666666667n + n2 = 0 + 660

Combine like terms: -660 + 660 = 0
0 + 0.6666666667n + n2 = 0 + 660
0.6666666667n + n2 = 0 + 660

Combine like terms: 0 + 660 = 660
0.6666666667n + n2 = 660

The n term is 0.6666666667n.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667n + 0.1111111112 + n2 = 660 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667n + n2 = 660 + 0.1111111112

Combine like terms: 660 + 0.1111111112 = 660.1111111112
0.1111111112 + 0.6666666667n + n2 = 660.1111111112

Factor a perfect square on the left side:
(n + 0.3333333334)(n + 0.3333333334) = 660.1111111112

Calculate the square root of the right side: 25.692627563

Break this problem into two subproblems by setting 
(n + 0.3333333334) equal to 25.692627563 and -25.692627563.


Subproblem 1
n + 0.3333333334 = 25.692627563

Simplifying
n + 0.3333333334 = 25.692627563

Reorder the terms:
0.3333333334 + n = 25.692627563

Solving
0.3333333334 + n = 25.692627563

Solving for variable 'n'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + n = 25.692627563 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + n = 25.692627563 + -0.3333333334
n = 25.692627563 + -0.3333333334

Combine like terms: 25.692627563 + -0.3333333334 = 25.3592942296
n = 25.3592942296

Simplifying
n = 25.3592942296


Subproblem 2
n + 0.3333333334 = -25.692627563

Simplifying
n + 0.3333333334 = -25.692627563

Reorder the terms:
0.3333333334 + n = -25.692627563

Solving
0.3333333334 + n = -25.692627563

Solving for variable 'n'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + n = -25.692627563 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + n = -25.692627563 + -0.3333333334
n = -25.692627563 + -0.3333333334

Combine like terms: -25.692627563 + -0.3333333334 = -26.0259608964
n = -26.0259608964

Simplifying
n = -26.0259608964


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {25.3592942296, -26.0259608964}

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