0=x^4-3x^3+7x^2

Solution for 0=x^4-3x^3+7x^2 equation:

Simplifying
0 = x4 + -3x3 + 7x2

Reorder the terms:
0 = 7x2 + -3x3 + x4

Solving
0 = 7x2 + -3x3 + x4

Solving for variable 'x'.
Remove the zero:
-7x2 + 3x3 + -1x4 = 7x2 + -3x3 + x4 + -7x2 + 3x3 + -1x4

Reorder the terms:
-7x2 + 3x3 + -1x4 = 7x2 + -7x2 + -3x3 + 3x3 + x4 + -1x4

Combine like terms: 7x2 + -7x2 = 0
-7x2 + 3x3 + -1x4 = 0 + -3x3 + 3x3 + x4 + -1x4
-7x2 + 3x3 + -1x4 = -3x3 + 3x3 + x4 + -1x4

Combine like terms: -3x3 + 3x3 = 0
-7x2 + 3x3 + -1x4 = 0 + x4 + -1x4
-7x2 + 3x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-7x2 + 3x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-7 + 3x + -1x2) = 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 '(-7 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-7 + 3x + -1x2 = 0

Solving
-7 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
7 + -3x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -3x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -3x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x + x2 = 0 + -7
-3x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-3x + x2 = -7

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -7 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -7 + 2.25

Combine like terms: -7 + 2.25 = -4.75
2.25 + -3x + x2 = -4.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -4.75

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}