0=x^4+x^3-6x^2

Solution for 0=x^4+x^3-6x^2 equation:

Simplifying
0 = x4 + x3 + -6x2

Reorder the terms:
0 = -6x2 + x3 + x4

Solving
0 = -6x2 + x3 + x4

Solving for variable 'x'.
Remove the zero:
6x2 + -1x3 + -1x4 = -6x2 + x3 + x4 + 6x2 + -1x3 + -1x4

Reorder the terms:
6x2 + -1x3 + -1x4 = -6x2 + 6x2 + x3 + -1x3 + x4 + -1x4

Combine like terms: -6x2 + 6x2 = 0
6x2 + -1x3 + -1x4 = 0 + x3 + -1x3 + x4 + -1x4
6x2 + -1x3 + -1x4 = x3 + -1x3 + x4 + -1x4

Combine like terms: x3 + -1x3 = 0
6x2 + -1x3 + -1x4 = 0 + x4 + -1x4
6x2 + -1x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
6x2 + -1x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + -1x + -1x2) = 0

Factor a trinomial.
x2((2 + -1x)(3 + x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

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

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

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

Simplifying
x = -3
Solution
x = {0, 2, -3}