Solve B=(3x-3)(2x+7)-(9x^2-9)

$$B = ( 3 x - 3 ) ( 2 x + 7 ) - ( 9 x ^ { 2 } - 9 )$$

Solve for B

$$B=3\left(4-x\right)\left(x-1\right)$$

Solution Steps

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

$$B=6x^{2}+15x-21-\left(9x^{2}-9\right)$$

To find the opposite of 9x^{2}-9, find the opposite of each term.

$$B=6x^{2}+15x-21-9x^{2}+9$$

Combine 6x^{2} and -9x^{2} to get -3x^{2}.

$$B=-3x^{2}+15x-21+9$$

Add -21 and 9 to get -12.

$$B=-3x^{2}+15x-12$$

Solve for x (complex solution)

$$x=\frac{\sqrt{81-12B}}{6}+\frac{5}{2}$$

$$x=-\frac{\sqrt{81-12B}}{6}+\frac{5}{2}$$

Solve for x

$$x=\frac{\sqrt{81-12B}}{6}+\frac{5}{2}$$

$$x=-\frac{\sqrt{81-12B}}{6}+\frac{5}{2}\text{, }B\leq \frac{27}{4}$$