-12x^2-240x+819=0

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Solution for -12x^2-240x+819=0 equation: 


Simplifying
-12x2 + -240x + 819 = 0

Reorder the terms:
819 + -240x + -12x2 = 0

Solving
819 + -240x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(273 + -80x + -4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(273 + -80x + -4x2)' equal to zero and attempt to solve:

Simplifying
273 + -80x + -4x2 = 0

Solving
273 + -80x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-68.25 + 20x + x2 = 0

Move the constant term to the right:

Add '68.25' to each side of the equation.
-68.25 + 20x + 68.25 + x2 = 0 + 68.25

Reorder the terms:
-68.25 + 68.25 + 20x + x2 = 0 + 68.25

Combine like terms: -68.25 + 68.25 = 0.00
0.00 + 20x + x2 = 0 + 68.25
20x + x2 = 0 + 68.25

Combine like terms: 0 + 68.25 = 68.25
20x + x2 = 68.25

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 68.25 + 100

Reorder the terms:
100 + 20x + x2 = 68.25 + 100

Combine like terms: 68.25 + 100 = 168.25
100 + 20x + x2 = 168.25

Factor a perfect square on the left side:
(x + 10)(x + 10) = 168.25

Calculate the square root of the right side: 12.971121771

Break this problem into two subproblems by setting 
(x + 10) equal to 12.971121771 and -12.971121771.


Subproblem 1
x + 10 = 12.971121771

Simplifying
x + 10 = 12.971121771

Reorder the terms:
10 + x = 12.971121771

Solving
10 + x = 12.971121771

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 12.971121771 + -10

Combine like terms: 10 + -10 = 0
0 + x = 12.971121771 + -10
x = 12.971121771 + -10

Combine like terms: 12.971121771 + -10 = 2.971121771
x = 2.971121771

Simplifying
x = 2.971121771


Subproblem 2
x + 10 = -12.971121771

Simplifying
x + 10 = -12.971121771

Reorder the terms:
10 + x = -12.971121771

Solving
10 + x = -12.971121771

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -12.971121771 + -10

Combine like terms: 10 + -10 = 0
0 + x = -12.971121771 + -10
x = -12.971121771 + -10

Combine like terms: -12.971121771 + -10 = -22.971121771
x = -22.971121771

Simplifying
x = -22.971121771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.971121771, -22.971121771}
Solution
x = {2.971121771, -22.971121771}

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