Solve B=(-4x+7)(7-3x)+(x-9)(11+6x)

$$B = ( - 4 x + 7 ) ( 7 - 3 x ) + ( x - 9 ) ( 11 + 6 x )$$

Solve for B

$$B=18x^{2}-92x-50$$

Solution Steps

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

$$B=-49x+12x^{2}+49+\left(x-9\right)\left(11+6x\right)$$

Use the distributive property to multiply x-9 by 11+6x and combine like terms.

$$B=-49x+12x^{2}+49-43x+6x^{2}-99$$

Combine -49x and -43x to get -92x.

$$B=-92x+12x^{2}+49+6x^{2}-99$$

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

$$B=-92x+18x^{2}+49-99$$

Subtract 99 from 49 to get -50.

$$B=-92x+18x^{2}-50$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{18B+3016}}{18}+\frac{23}{9}$$

$$x=\frac{\sqrt{18B+3016}}{18}+\frac{23}{9}$$

Solve for x

$$x=-\frac{\sqrt{18B+3016}}{18}+\frac{23}{9}$$

$$x=\frac{\sqrt{18B+3016}}{18}+\frac{23}{9}\text{, }B\geq -\frac{1508}{9}$$