Solve B=(x+4)(3x-2)-(7x+4)(3x-2)

$$B = ( x + 4 ) ( 3 x - 2 ) - ( 7 x + 4 ) ( 3 x - 2 )$$

Solve for B

$$B=-6x\left(3x-2\right)$$

Solution Steps

Use the distributive property to multiply x+4 by 3x-2 and combine like terms.

$$B=3x^{2}+10x-8-\left(7x+4\right)\left(3x-2\right)$$

Use the distributive property to multiply 7x+4 by 3x-2 and combine like terms.

$$B=3x^{2}+10x-8-\left(21x^{2}-2x-8\right)$$

To find the opposite of 21x^{2}-2x-8, find the opposite of each term.

$$B=3x^{2}+10x-8-21x^{2}+2x+8$$

Combine 3x^{2} and -21x^{2} to get -18x^{2}.

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

Combine 10x and 2x to get 12x.

$$B=-18x^{2}+12x-8+8$$

Add -8 and 8 to get 0.

$$B=-18x^{2}+12x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4-2B}}{6}+\frac{1}{3}$$

$$x=-\frac{\sqrt{4-2B}}{6}+\frac{1}{3}$$

Solve for x

$$x=\frac{\sqrt{4-2B}}{6}+\frac{1}{3}$$

$$x=-\frac{\sqrt{4-2B}}{6}+\frac{1}{3}\text{, }B\leq 2$$