0=x^4-10x^3+25x^2

Solution for 0=x^4-10x^3+25x^2 equation:

Simplifying
0 = x4 + -10x3 + 25x2

Reorder the terms:
0 = 25x2 + -10x3 + x4

Solving
0 = 25x2 + -10x3 + x4

Solving for variable 'x'.
Remove the zero:
-25x2 + 10x3 + -1x4 = 25x2 + -10x3 + x4 + -25x2 + 10x3 + -1x4

Reorder the terms:
-25x2 + 10x3 + -1x4 = 25x2 + -25x2 + -10x3 + 10x3 + x4 + -1x4

Combine like terms: 25x2 + -25x2 = 0
-25x2 + 10x3 + -1x4 = 0 + -10x3 + 10x3 + x4 + -1x4
-25x2 + 10x3 + -1x4 = -10x3 + 10x3 + x4 + -1x4

Combine like terms: -10x3 + 10x3 = 0
-25x2 + 10x3 + -1x4 = 0 + x4 + -1x4
-25x2 + 10x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-25x2 + 10x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-25 + 10x + -1x2) = 0

Factor a trinomial.
x2((-5 + x)(5 + -1x)) = 0

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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 5, 5}