-3x^2+180x-1800=0

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Solution for -3x^2+180x-1800=0 equation: 


Simplifying
-3x2 + 180x + -1800 = 0

Reorder the terms:
-1800 + 180x + -3x2 = 0

Solving
-1800 + 180x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-600 + 60x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-600 + 60x + -1x2)' equal to zero and attempt to solve:

Simplifying
-600 + 60x + -1x2 = 0

Solving
-600 + 60x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
600 + -60x + x2 = 0

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -60x + -600 + x2 = 0 + -600

Reorder the terms:
600 + -600 + -60x + x2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -60x + x2 = 0 + -600
-60x + x2 = 0 + -600

Combine like terms: 0 + -600 = -600
-60x + x2 = -600

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = -600 + 900

Reorder the terms:
900 + -60x + x2 = -600 + 900

Combine like terms: -600 + 900 = 300
900 + -60x + x2 = 300

Factor a perfect square on the left side:
(x + -30)(x + -30) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + -30) equal to 17.320508076 and -17.320508076.


Subproblem 1
x + -30 = 17.320508076

Simplifying
x + -30 = 17.320508076

Reorder the terms:
-30 + x = 17.320508076

Solving
-30 + x = 17.320508076

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = 17.320508076 + 30

Combine like terms: -30 + 30 = 0
0 + x = 17.320508076 + 30
x = 17.320508076 + 30

Combine like terms: 17.320508076 + 30 = 47.320508076
x = 47.320508076

Simplifying
x = 47.320508076


Subproblem 2
x + -30 = -17.320508076

Simplifying
x + -30 = -17.320508076

Reorder the terms:
-30 + x = -17.320508076

Solving
-30 + x = -17.320508076

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = -17.320508076 + 30

Combine like terms: -30 + 30 = 0
0 + x = -17.320508076 + 30
x = -17.320508076 + 30

Combine like terms: -17.320508076 + 30 = 12.679491924
x = 12.679491924

Simplifying
x = 12.679491924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.320508076, 12.679491924}
Solution
x = {47.320508076, 12.679491924}

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