28t^4-35t^3+14t^2=0

Solution for 28t^4-35t^3+14t^2=0 equation:

Simplifying
28t4 + -35t3 + 14t2 = 0

Reorder the terms:
14t2 + -35t3 + 28t4 = 0

Solving
14t2 + -35t3 + 28t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '7t2'.
7t2(2 + -5t + 4t2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
Set the factor '(2 + -5t + 4t2)' equal to zero and attempt to solve:

Simplifying
2 + -5t + 4t2 = 0

Solving
2 + -5t + 4t2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.5 + -1.25t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.25t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.25t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.25t + t2 = 0 + -0.5
-1.25t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.25t + t2 = -0.5

The t term is -1.25t.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25t + 0.390625 + t2 = -0.5 + 0.390625

Reorder the terms:
0.390625 + -1.25t + t2 = -0.5 + 0.390625

Combine like terms: -0.5 + 0.390625 = -0.109375
0.390625 + -1.25t + t2 = -0.109375

Factor a perfect square on the left side:
(t + -0.625)(t + -0.625) = -0.109375

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}