Simplify (3x^2+2y^2-3x)+(2x^2+y^2-2x)-(x^2+3y^2+x)

$(3 x^{2} + 2 y^{2} - 3 x) + (2 x^{2} + y^{2} - 2 x) - (x^{2} + 3 y^{2} + x)$

Remove parentheses.

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - (x^{2} + 3 y^{2} + x)$

Simplify each term.

Apply the distributive property.

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - x^{2} - (3 y^{2}) - x$

Multiply $3$ by $- 1$ .

$3 x^{2} + 2 y^{2} - 3 x + 2 x^{2} + y^{2} - 2 x - x^{2} - 3 y^{2} - x$

Simplify by adding terms.

Add $3 x^{2}$ and $2 x^{2}$ .

$5 x^{2} + 2 y^{2} - 3 x + y^{2} - 2 x - x^{2} - 3 y^{2} - x$

Subtract $x^{2}$ from $5 x^{2}$ .

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

Add $2 y^{2}$ and $y^{2}$ .

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

Combine the opposite terms in $4 x^{2} + 3 y^{2} - 3 x - 2 x - 3 y^{2} - x$ .

Subtract $3 y^{2}$ from $3 y^{2}$ .

$4 x^{2} - 3 x - 2 x + 0 - x$

Add $4 x^{2} - 3 x - 2 x$ and $0$ .

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

Subtract $2 x$ from $- 3 x$ .

$4 x^{2} - 5 x - x$

Subtract $x$ from $- 5 x$ .

$4 x^{2} - 6 x$