6x^2-2400x+180000=0

Solution for 6x^2-2400x+180000=0 equation:

Simplifying
6x2 + -2400x + 180000 = 0

Reorder the terms:
180000 + -2400x + 6x2 = 0

Solving
180000 + -2400x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(30000 + -400x + x2) = 0

Factor a trinomial.
6((100 + -1x)(300 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Subproblem 2
Set the factor '(300 + -1x)' equal to zero and attempt to solve:

Simplifying
300 + -1x = 0

Solving
300 + -1x = 0

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

Add '-300' to each side of the equation.
300 + -300 + -1x = 0 + -300

Combine like terms: 300 + -300 = 0
0 + -1x = 0 + -300
-1x = 0 + -300

Combine like terms: 0 + -300 = -300
-1x = -300

Divide each side by '-1'.
x = 300

Simplifying
x = 300
Solution
x = {100, 300}