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

$(- 6 x^{3} + 2 x^{2} + 4) + (x^{4} - 6 x^{3} - 2 x)$

Remove parentheses.

$- 6 x^{3} + 2 x^{2} + 4 + x^{4} - 6 x^{3} - 2 x$

Subtract $6 x^{3}$ from $- 6 x^{3}$ .

$- 12 x^{3} + 2 x^{2} + 4 + x^{4} - 2 x$

Simplify the expression.

Move $4$ .

$- 12 x^{3} + 2 x^{2} + x^{4} - 2 x + 4$

Move $2 x^{2}$ .

$- 12 x^{3} + x^{4} + 2 x^{2} - 2 x + 4$

Reorder $- 12 x^{3}$ and $x^{4}$ .

$x^{4} - 12 x^{3} + 2 x^{2} - 2 x + 4$