Solve -2(3x+4)-7(2x+3)-[-2*(3x+4)-6x(x-2)]-12

$$- 2 ( 3 x + 4 ) - 7 ( 2 x + 3 ) - [ - 2 \cdot ( 3 x + 4 ) - 6 x ( x - 2 ) ] - 12$$

Evaluate

$$6x^{2}-26x-33$$

Solution Steps

Use the distributive property to multiply -2 by 3x+4.

$$-6x-8-7\left(2x+3\right)-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -7 by 2x+3.

$$-6x-8-14x-21-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Combine -6x and -14x to get -20x.

$$-20x-8-21-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Subtract 21 from -8 to get -29.

$$-20x-29-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -2 by 3x+4.

$$-20x-29-\left(-6x-8-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -6x by x-2.

$$-20x-29-\left(-6x-8-6x^{2}+12x\right)-12$$

Combine -6x and 12x to get 6x.

$$-20x-29-\left(6x-8-6x^{2}\right)-12$$

To find the opposite of 6x-8-6x^{2}, find the opposite of each term.

$$-20x-29-6x-\left(-8\right)-\left(-6x^{2}\right)-12$$

The opposite of -8 is 8.

$$-20x-29-6x+8-\left(-6x^{2}\right)-12$$

The opposite of -6x^{2} is 6x^{2}.

$$-20x-29-6x+8+6x^{2}-12$$

Combine -20x and -6x to get -26x.

$$-26x-29+8+6x^{2}-12$$

Add -29 and 8 to get -21.

$$-26x-21+6x^{2}-12$$

Subtract 12 from -21 to get -33.

$$-26x-33+6x^{2}$$

Expand

$$6x^{2}-26x-33$$

Solution Steps

Use the distributive property to multiply -2 by 3x+4.

$$-6x-8-7\left(2x+3\right)-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -7 by 2x+3.

$$-6x-8-14x-21-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Combine -6x and -14x to get -20x.

$$-20x-8-21-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Subtract 21 from -8 to get -29.

$$-20x-29-\left(-2\left(3x+4\right)-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -2 by 3x+4.

$$-20x-29-\left(-6x-8-6x\left(x-2\right)\right)-12$$

Use the distributive property to multiply -6x by x-2.

$$-20x-29-\left(-6x-8-6x^{2}+12x\right)-12$$

Combine -6x and 12x to get 6x.

$$-20x-29-\left(6x-8-6x^{2}\right)-12$$

To find the opposite of 6x-8-6x^{2}, find the opposite of each term.

$$-20x-29-6x-\left(-8\right)-\left(-6x^{2}\right)-12$$

The opposite of -8 is 8.

$$-20x-29-6x+8-\left(-6x^{2}\right)-12$$

The opposite of -6x^{2} is 6x^{2}.

$$-20x-29-6x+8+6x^{2}-12$$

Combine -20x and -6x to get -26x.

$$-26x-29+8+6x^{2}-12$$

Add -29 and 8 to get -21.

$$-26x-21+6x^{2}-12$$

Subtract 12 from -21 to get -33.

$$-26x-33+6x^{2}$$