# Solve for x x^3-4x^2+4x=0 x3-4×2+4x=0
Factor the left side of the equation.
Factor x out of x3-4×2+4x.
Factor x out of x3.
x⋅x2-4×2+4x=0
Factor x out of -4×2.
x⋅x2+x(-4x)+4x=0
Factor x out of 4x.
x⋅x2+x(-4x)+x⋅4=0
Factor x out of x⋅x2+x(-4x).
x(x2-4x)+x⋅4=0
Factor x out of x(x2-4x)+x⋅4.
x(x2-4x+4)=0
x(x2-4x+4)=0
Factor using the perfect square rule.
Rewrite 4 as 22.
x(x2-4x+22)=0
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅x⋅-2
Simplify.
2ab=-4x
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=x and b=-2.
x(x-2)2=0
x(x-2)2=0
x(x-2)2=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x=0
(x-2)2=0
Set the first factor equal to 0.
x=0
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
(x-2)2=0
Set the x-2 equal to 0.
x-2=0
Add 2 to both sides of the equation.
x=2
x=2
The final solution is all the values that make x(x-2)2=0 true.
x=0,2
Solve for x x^3-4x^2+4x=0     