-3x^2-1800x+202500=0

Solution for -3x^2-1800x+202500=0 equation:

Simplifying
-3x2 + -1800x + 202500 = 0

Reorder the terms:
202500 + -1800x + -3x2 = 0

Solving
202500 + -1800x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(67500 + -600x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(67500 + -600x + -1x2)' equal to zero and attempt to solve:

Simplifying
67500 + -600x + -1x2 = 0

Solving
67500 + -600x + -1x2 = 0

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

Divide each side by '-1'.
-67500 + 600x + x2 = 0

Move the constant term to the right:

Add '67500' to each side of the equation.
-67500 + 600x + 67500 + x2 = 0 + 67500

Reorder the terms:
-67500 + 67500 + 600x + x2 = 0 + 67500

Combine like terms: -67500 + 67500 = 0
0 + 600x + x2 = 0 + 67500
600x + x2 = 0 + 67500

Combine like terms: 0 + 67500 = 67500
600x + x2 = 67500

The x term is 600x.  Take half its coefficient (300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
600x + 90000 + x2 = 67500 + 90000

Reorder the terms:
90000 + 600x + x2 = 67500 + 90000

Combine like terms: 67500 + 90000 = 157500
90000 + 600x + x2 = 157500

Factor a perfect square on the left side:
(x + 300)(x + 300) = 157500

Calculate the square root of the right side: 396.86269666

Break this problem into two subproblems by setting 
(x + 300) equal to 396.86269666 and -396.86269666.

Subproblem 1
x + 300 = 396.86269666

Simplifying
x + 300 = 396.86269666

Reorder the terms:
300 + x = 396.86269666

Solving
300 + x = 396.86269666

Solving for variable 'x'.

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

Add '-300' to each side of the equation.
300 + -300 + x = 396.86269666 + -300

Combine like terms: 300 + -300 = 0
0 + x = 396.86269666 + -300
x = 396.86269666 + -300

Combine like terms: 396.86269666 + -300 = 96.86269666
x = 96.86269666

Simplifying
x = 96.86269666

Subproblem 2
x + 300 = -396.86269666

Simplifying
x + 300 = -396.86269666

Reorder the terms:
300 + x = -396.86269666

Solving
300 + x = -396.86269666

Solving for variable 'x'.

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

Add '-300' to each side of the equation.
300 + -300 + x = -396.86269666 + -300

Combine like terms: 300 + -300 = 0
0 + x = -396.86269666 + -300
x = -396.86269666 + -300

Combine like terms: -396.86269666 + -300 = -696.86269666
x = -696.86269666

Simplifying
x = -696.86269666

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {96.86269666, -696.86269666}
Solution
x = {96.86269666, -696.86269666}