Solve (3x+1)(4x-5)+(3-2x)(1+6x)

$$( 3 x + 1 ) ( 4 x - 5 ) + ( 3 - 2 x ) ( 1 + 6 x )$$

Evaluate

$$5x-2$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+1 by each term of 4x-5.

$$12x^{2}-15x+4x-5+\left(3-2x\right)\left(1+6x\right)$$

Combine -15x and 4x to get -11x.

$$12x^{2}-11x-5+\left(3-2x\right)\left(1+6x\right)$$

Apply the distributive property by multiplying each term of 3-2x by each term of 1+6x.

$$12x^{2}-11x-5+3+18x-2x-12x^{2}$$

Combine 18x and -2x to get 16x.

$$12x^{2}-11x-5+3+16x-12x^{2}$$

Add -5 and 3 to get -2.

$$12x^{2}-11x-2+16x-12x^{2}$$

Combine -11x and 16x to get 5x.

$$12x^{2}+5x-2-12x^{2}$$

Combine 12x^{2} and -12x^{2} to get 0.

$$5x-2$$

Expand

$$5x-2$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+1 by each term of 4x-5.

$$12x^{2}-15x+4x-5+\left(3-2x\right)\left(1+6x\right)$$

Combine -15x and 4x to get -11x.

$$12x^{2}-11x-5+\left(3-2x\right)\left(1+6x\right)$$

Apply the distributive property by multiplying each term of 3-2x by each term of 1+6x.

$$12x^{2}-11x-5+3+18x-2x-12x^{2}$$

Combine 18x and -2x to get 16x.

$$12x^{2}-11x-5+3+16x-12x^{2}$$

Add -5 and 3 to get -2.

$$12x^{2}-11x-2+16x-12x^{2}$$

Combine -11x and 16x to get 5x.

$$12x^{2}+5x-2-12x^{2}$$

Combine 12x^{2} and -12x^{2} to get 0.

$$5x-2$$