Simplify -x^2-(3x-(12x^2-7x))-(2+(-2x-2))

$- x^{2} - (3 x - (12 x^{2} - 7 x)) - (2 + (- 2 x - 2))$

Step 1

Simplify by adding terms.

Remove parentheses.

$- x^{2} - (3 x - (12 x^{2} - 7 x)) - (2 - 2 x - 2)$

Combine the opposite terms in $- x^{2} - (3 x - (12 x^{2} - 7 x)) - (2 - 2 x - 2)$ .

Subtract $2$ from $2$ .

$- x^{2} - (3 x - (12 x^{2} - 7 x)) - (- 2 x + 0)$

Add $- 2 x$ and $0$ .

$- x^{2} - (3 x - (12 x^{2} - 7 x)) - (- 2 x)$

Step 2

Simplify each term.

Apply the distributive property.

$- x^{2} - (3 x - (12 x^{2}) - (- 7 x)) - (- 2 x)$

Multiply $12$ by $- 1$ .

$- x^{2} - (3 x - 12 x^{2} - (- 7 x)) - (- 2 x)$

Multiply $- 7$ by $- 1$ .

$- x^{2} - (3 x - 12 x^{2} + 7 x) - (- 2 x)$

Add $3 x$ and $7 x$ .

$- x^{2} - (- 12 x^{2} + 10 x) - (- 2 x)$

Apply the distributive property.

$- x^{2} - (- 12 x^{2}) - (10 x) - (- 2 x)$

Multiply $- 12$ by $- 1$ .

$- x^{2} + 12 x^{2} - (10 x) - (- 2 x)$

Multiply $10$ by $- 1$ .

$- x^{2} + 12 x^{2} - 10 x - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$- x^{2} + 12 x^{2} - 10 x + 2 x$

Step 3

Simplify by adding terms.

Add $- x^{2}$ and $12 x^{2}$ .

$11 x^{2} - 10 x + 2 x$

Add $- 10 x$ and $2 x$ .

$11 x^{2} - 8 x$