Simplify (4x-6x^2-7)-(2+7x-5x^2)

$(4 x - 6 x^{2} - 7) - (2 + 7 x - 5 x^{2})$

Step 1

Simplify each term.

Apply the distributive property.

$4 x - 6 x^{2} - 7 - 1 \cdot 2 - (7 x) - (- 5 x^{2})$

Simplify.

Multiply $- 1$ by $2$ .

$4 x - 6 x^{2} - 7 - 2 - (7 x) - (- 5 x^{2})$

Multiply $7$ by $- 1$ .

$4 x - 6 x^{2} - 7 - 2 - 7 x - (- 5 x^{2})$

Multiply $- 5$ by $- 1$ .

$4 x - 6 x^{2} - 7 - 2 - 7 x + 5 x^{2}$

Step 2

Simplify by adding terms.

Subtract $7 x$ from $4 x$ .

$- 3 x - 6 x^{2} - 7 - 2 + 5 x^{2}$

Add $- 6 x^{2}$ and $5 x^{2}$ .

$- 3 x - x^{2} - 7 - 2$

Simplify the expression.

Subtract $2$ from $- 7$ .

$- 3 x - x^{2} - 9$

Reorder $- 3 x$ and $- x^{2}$ .

$- x^{2} - 3 x - 9$