-x^4+3x^3-18x^2=0

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Solution for -x^4+3x^3-18x^2=0 equation: 


Simplifying
-1x4 + 3x3 + -18x2 = 0

Reorder the terms:
-18x2 + 3x3 + -1x4 = 0

Solving
-18x2 + 3x3 + -1x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-18 + 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 '(-18 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-18 + 3x + -1x2 = 0

Solving
-18 + 3x + -1x2 = 0

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

Divide each side by '-1'.
18 + -3x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -3x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -3x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -3x + x2 = 0 + -18
-3x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-3x + x2 = -18

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 = -18 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -18 + 2.25

Combine like terms: -18 + 2.25 = -15.75
2.25 + -3x + x2 = -15.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -15.75

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}

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