28x^4-42x^3+35x^2=0

Solution for 28x^4-42x^3+35x^2=0 equation:

Simplifying
28x4 + -42x3 + 35x2 = 0

Reorder the terms:
35x2 + -42x3 + 28x4 = 0

Solving
35x2 + -42x3 + 28x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x2'.
7x2(5 + -6x + 4x2) = 0

Ignore the factor 7.
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 '(5 + -6x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + -6x + 4x2 = 0

Solving
5 + -6x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -1.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -1.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -1.5x + x2 = 0 + -1.25
-1.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-1.5x + x2 = -1.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -1.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1.25 + 0.5625

Combine like terms: -1.25 + 0.5625 = -0.6875
0.5625 + -1.5x + x2 = -0.6875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.6875

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
x = {0}