0=t^3-4t^2+4t

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Solution for 0=t^3-4t^2+4t equation: 


Simplifying
0 = t3 + -4t2 + 4t

Reorder the terms:
0 = 4t + -4t2 + t3

Solving
0 = 4t + -4t2 + t3

Solving for variable 't'.
Remove the zero:
-4t + 4t2 + -1t3 = 4t + -4t2 + t3 + -4t + 4t2 + -1t3

Reorder the terms:
-4t + 4t2 + -1t3 = 4t + -4t + -4t2 + 4t2 + t3 + -1t3

Combine like terms: 4t + -4t = 0
-4t + 4t2 + -1t3 = 0 + -4t2 + 4t2 + t3 + -1t3
-4t + 4t2 + -1t3 = -4t2 + 4t2 + t3 + -1t3

Combine like terms: -4t2 + 4t2 = 0
-4t + 4t2 + -1t3 = 0 + t3 + -1t3
-4t + 4t2 + -1t3 = t3 + -1t3

Combine like terms: t3 + -1t3 = 0
-4t + 4t2 + -1t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-4 + 4t + -1t2) = 0

Factor a trinomial.
t((-2 + t)(2 + -1t)) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(-2 + t)' equal to zero and attempt to solve:

Simplifying
-2 + t = 0

Solving
-2 + t = 0

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

Add '2' to each side of the equation.
-2 + 2 + t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + t = 0 + 2
t = 0 + 2

Combine like terms: 0 + 2 = 2
t = 2

Simplifying
t = 2

Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0, 2, 2}

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