Solve B=5(5-2x)(x+1)+5(8x-5)(x+1)

$$B = 5 ( 5 - 2 x ) ( x + 1 ) + 5 ( 8 x - 5 ) ( x + 1 )$$

Solve for B

$$B=30x\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply 5 by 5-2x.

$$B=\left(25-10x\right)\left(x+1\right)+5\left(8x-5\right)\left(x+1\right)$$

Use the distributive property to multiply 25-10x by x+1 and combine like terms.

$$B=15x+25-10x^{2}+5\left(8x-5\right)\left(x+1\right)$$

Use the distributive property to multiply 5 by 8x-5.

$$B=15x+25-10x^{2}+\left(40x-25\right)\left(x+1\right)$$

Use the distributive property to multiply 40x-25 by x+1 and combine like terms.

$$B=15x+25-10x^{2}+40x^{2}+15x-25$$

Combine -10x^{2} and 40x^{2} to get 30x^{2}.

$$B=15x+25+30x^{2}+15x-25$$

Combine 15x and 15x to get 30x.

$$B=30x+25+30x^{2}-25$$

Subtract 25 from 25 to get 0.

$$B=30x+30x^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30B+225}}{30}-\frac{1}{2}$$

$$x=\frac{\sqrt{30B+225}}{30}-\frac{1}{2}$$

Solve for x

$$x=-\frac{\sqrt{30B+225}}{30}-\frac{1}{2}$$

$$x=\frac{\sqrt{30B+225}}{30}-\frac{1}{2}\text{, }B\geq -\frac{15}{2}$$