5x^4-3x^3+4x^2=0

Solution for 5x^4-3x^3+4x^2=0 equation:

Simplifying
5x4 + -3x3 + 4x2 = 0

Reorder the terms:
4x2 + -3x3 + 5x4 = 0

Solving
4x2 + -3x3 + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -3x + 5x2) = 0

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 '(4 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x + 5x2 = 0

Solving
4 + -3x + 5x2 = 0

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

Divide each side by '5'.
0.8 + -0.6x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -0.6x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -0.6x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -0.6x + x2 = 0 + -0.8
-0.6x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-0.6x + x2 = -0.8

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -0.8 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -0.8 + 0.09

Combine like terms: -0.8 + 0.09 = -0.71
0.09 + -0.6x + x2 = -0.71

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = -0.71

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}