Simplify 3(x^2-2x+3)-4(4x+1)-(3x^2-2x)

$3 (x^{2} - 2 x + 3) - 4 (4 x + 1) - (3 x^{2} - 2 x)$

Step 1

Simplify each term.

Apply the distributive property.

$3 x^{2} + 3 (- 2 x) + 3 \cdot 3 - 4 (4 x + 1) - (3 x^{2} - 2 x)$

Simplify.

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x + 3 \cdot 3 - 4 (4 x + 1) - (3 x^{2} - 2 x)$

Multiply $3$ by $3$ .

$3 x^{2} - 6 x + 9 - 4 (4 x + 1) - (3 x^{2} - 2 x)$

Apply the distributive property.

$3 x^{2} - 6 x + 9 - 4 (4 x) - 4 \cdot 1 - (3 x^{2} - 2 x)$

Multiply $4$ by $- 4$ .

$3 x^{2} - 6 x + 9 - 16 x - 4 \cdot 1 - (3 x^{2} - 2 x)$

Multiply $- 4$ by $1$ .

$3 x^{2} - 6 x + 9 - 16 x - 4 - (3 x^{2} - 2 x)$

Apply the distributive property.

$3 x^{2} - 6 x + 9 - 16 x - 4 - (3 x^{2}) - (- 2 x)$

Multiply $3$ by $- 1$ .

$3 x^{2} - 6 x + 9 - 16 x - 4 - 3 x^{2} - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$3 x^{2} - 6 x + 9 - 16 x - 4 - 3 x^{2} + 2 x$

Step 2

Simplify by adding terms.

Combine the opposite terms in $3 x^{2} - 6 x + 9 - 16 x - 4 - 3 x^{2} + 2 x$ .

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

$- 6 x + 9 - 16 x - 4 + 0 + 2 x$

Add $- 6 x + 9 - 16 x - 4$ and $0$ .

$- 6 x + 9 - 16 x - 4 + 2 x$

Subtract $16 x$ from $- 6 x$ .

$- 22 x + 9 - 4 + 2 x$

Add $- 22 x$ and $2 x$ .

$- 20 x + 9 - 4$

Subtract $4$ from $9$ .

$- 20 x + 5$