(2x^4+x^3-6x^2)-(-x^2+3+x^3)=

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

Simplifying
(2x4 + x3 + -6x2) + -1(-1x2 + 3 + x3) = 0

Reorder the terms:
(-6x2 + x3 + 2x4) + -1(-1x2 + 3 + x3) = 0

Remove parenthesis around (-6x2 + x3 + 2x4)
-6x2 + x3 + 2x4 + -1(-1x2 + 3 + x3) = 0

Reorder the terms:
-6x2 + x3 + 2x4 + -1(3 + -1x2 + x3) = 0
-6x2 + x3 + 2x4 + (3 * -1 + -1x2 * -1 + x3 * -1) = 0
-6x2 + x3 + 2x4 + (-3 + 1x2 + -1x3) = 0

Reorder the terms:
-3 + -6x2 + 1x2 + x3 + -1x3 + 2x4 = 0

Combine like terms: -6x2 + 1x2 = -5x2
-3 + -5x2 + x3 + -1x3 + 2x4 = 0

Combine like terms: x3 + -1x3 = 0
-3 + -5x2 + 0 + 2x4 = 0
-3 + -5x2 + 2x4 = 0

Solving
-3 + -5x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(-1 + -2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -2x2 = 0

Solving
-1 + -2x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x2 = 0 + 1
-2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2x2 = 1

Divide each side by '-2'.
x2 = -0.5

Simplifying
x2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

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

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}