4t(t^2-4t+420)=0

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Solution for 4t(t^2-4t+420)=0 equation: 


Simplifying
4t(t2 + -4t + 420) = 0

Reorder the terms:
4t(420 + -4t + t2) = 0
(420 * 4t + -4t * 4t + t2 * 4t) = 0
(1680t + -16t2 + 4t3) = 0

Solving
1680t + -16t2 + 4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t'.
4t(420 + -4t + t2) = 0

Ignore the factor 4.

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 '(420 + -4t + t2)' equal to zero and attempt to solve:

Simplifying
420 + -4t + t2 = 0

Solving
420 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-420' to each side of the equation.
420 + -4t + -420 + t2 = 0 + -420

Reorder the terms:
420 + -420 + -4t + t2 = 0 + -420

Combine like terms: 420 + -420 = 0
0 + -4t + t2 = 0 + -420
-4t + t2 = 0 + -420

Combine like terms: 0 + -420 = -420
-4t + t2 = -420

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -420 + 4

Reorder the terms:
4 + -4t + t2 = -420 + 4

Combine like terms: -420 + 4 = -416
4 + -4t + t2 = -416

Factor a perfect square on the left side:
(t + -2)(t + -2) = -416

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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