Solve B=(3x+2)(2x-5)-(6x-5)(4x+2)

$$B = ( 3 x + 2 ) ( 2 x - 5 ) - ( 6 x - 5 ) ( 4 x + 2 )$$

Solve for B

$$B=-3x\left(6x+1\right)$$

Solution Steps

Use the distributive property to multiply 3x+2 by 2x-5 and combine like terms.

$$B=6x^{2}-11x-10-\left(6x-5\right)\left(4x+2\right)$$

Use the distributive property to multiply 6x-5 by 4x+2 and combine like terms.

$$B=6x^{2}-11x-10-\left(24x^{2}-8x-10\right)$$

To find the opposite of 24x^{2}-8x-10, find the opposite of each term.

$$B=6x^{2}-11x-10-24x^{2}+8x+10$$

Combine 6x^{2} and -24x^{2} to get -18x^{2}.

$$B=-18x^{2}-11x-10+8x+10$$

Combine -11x and 8x to get -3x.

$$B=-18x^{2}-3x-10+10$$

Add -10 and 10 to get 0.

$$B=-18x^{2}-3x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1-8B}-1}{12}$$

$$x=\frac{-\sqrt{1-8B}-1}{12}$$

Solve for x

$$x=\frac{\sqrt{1-8B}-1}{12}$$

$$x=\frac{-\sqrt{1-8B}-1}{12}\text{, }B\leq \frac{1}{8}$$