120X^2-600X+720=0

Solution for 120X^2-600X+720=0 equation:

Simplifying
120X2 + -600X + 720 = 0

Reorder the terms:
720 + -600X + 120X2 = 0

Solving
720 + -600X + 120X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '120'.
120(6 + -5X + X2) = 0

Factor a trinomial.
120((2 + -1X)(3 + -1X)) = 0

Ignore the factor 120.
Subproblem 1
Set the factor '(2 + -1X)' equal to zero and attempt to solve:

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Subproblem 2
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Solution
X = {2, 3}