5X^4-15X^3+10X^2=0

Solution for 5X^4-15X^3+10X^2=0 equation:

Simplifying
5X4 + -15X3 + 10X2 = 0

Reorder the terms:
10X2 + -15X3 + 5X4 = 0

Solving
10X2 + -15X3 + 5X4 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '5X2'.
5X2(2 + -3X + X2) = 0

Factor a trinomial.
5X2((1 + -1X)(2 + -1X)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve:

Simplifying
X2 = 0

Solving
X2 = 0

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

Simplifying
X2 = 0

Take the square root of each side:
X = {0}
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
Subproblem 3
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
Solution
X = {0, 1, 2}