Solve left(6x-9right)left(-2x-5right)+left(-9+3xright)left(-9+6xright)

$$\left( 6x-9 \right) \left( -2x-5 \right) + \left( -9+3x \right) \left( -9+6x \right)$$

Evaluate

$$3\left(x-14\right)\left(2x-3\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 6x-9 by each term of -2x-5.

$$-12x^{2}-30x+18x+45+\left(-9+3x\right)\left(-9+6x\right)$$

Combine -30x and 18x to get -12x.

$$-12x^{2}-12x+45+\left(-9+3x\right)\left(-9+6x\right)$$

Apply the distributive property by multiplying each term of -9+3x by each term of -9+6x.

$$-12x^{2}-12x+45+81-54x-27x+18x^{2}$$

Combine -54x and -27x to get -81x.

$$-12x^{2}-12x+45+81-81x+18x^{2}$$

Add 45 and 81 to get 126.

$$-12x^{2}-12x+126-81x+18x^{2}$$

Combine -12x and -81x to get -93x.

$$-12x^{2}-93x+126+18x^{2}$$

Combine -12x^{2} and 18x^{2} to get 6x^{2}.

$$6x^{2}-93x+126$$

Expand

$$6x^{2}-93x+126$$

Solution Steps

Apply the distributive property by multiplying each term of 6x-9 by each term of -2x-5.

$$-12x^{2}-30x+18x+45+\left(-9+3x\right)\left(-9+6x\right)$$

Combine -30x and 18x to get -12x.

$$-12x^{2}-12x+45+\left(-9+3x\right)\left(-9+6x\right)$$

Apply the distributive property by multiplying each term of -9+3x by each term of -9+6x.

$$-12x^{2}-12x+45+81-54x-27x+18x^{2}$$

Combine -54x and -27x to get -81x.

$$-12x^{2}-12x+45+81-81x+18x^{2}$$

Add 45 and 81 to get 126.

$$-12x^{2}-12x+126-81x+18x^{2}$$

Combine -12x and -81x to get -93x.

$$-12x^{2}-93x+126+18x^{2}$$

Combine -12x^{2} and 18x^{2} to get 6x^{2}.

$$6x^{2}-93x+126$$