0=x^4-8x^3+16x^2

Solution for 0=x^4-8x^3+16x^2 equation:

Simplifying
0 = x4 + -8x3 + 16x2

Reorder the terms:
0 = 16x2 + -8x3 + x4

Solving
0 = 16x2 + -8x3 + x4

Solving for variable 'x'.
Remove the zero:
-16x2 + 8x3 + -1x4 = 16x2 + -8x3 + x4 + -16x2 + 8x3 + -1x4

Reorder the terms:
-16x2 + 8x3 + -1x4 = 16x2 + -16x2 + -8x3 + 8x3 + x4 + -1x4

Combine like terms: 16x2 + -16x2 = 0
-16x2 + 8x3 + -1x4 = 0 + -8x3 + 8x3 + x4 + -1x4
-16x2 + 8x3 + -1x4 = -8x3 + 8x3 + x4 + -1x4

Combine like terms: -8x3 + 8x3 = 0
-16x2 + 8x3 + -1x4 = 0 + x4 + -1x4
-16x2 + 8x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-16x2 + 8x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-16 + 8x + -1x2) = 0

Factor a trinomial.
x2((-4 + x)(4 + -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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4, 4}