63x^2-56x^3+14x^4=

Solution for 63x^2-56x^3+14x^4= equation:

Simplifying
63x2 + -56x3 + 14x4 = 0

Solving
63x2 + -56x3 + 14x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x2'.
7x2(9 + -8x + 2x2) = 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 '(9 + -8x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + -8x + 2x2 = 0

Solving
9 + -8x + 2x2 = 0

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

Divide each side by '2'.
4.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -4x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -4x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -4x + x2 = 0 + -4.5
-4x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-4x + x2 = -4.5

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

Add '4' to each side of the equation.
-4x + 4 + x2 = -4.5 + 4

Reorder the terms:
4 + -4x + x2 = -4.5 + 4

Combine like terms: -4.5 + 4 = -0.5
4 + -4x + x2 = -0.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = -0.5

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}