Solve P=3(4+x)(x+8)

$$P = 3 ( 4 + x ) ( x + 8 )$$

Solve for P

$$P=3\left(x+4\right)\left(x+8\right)$$

Solution Steps

Use the distributive property to multiply 3 by 4+x.

$$P=\left(12+3x\right)\left(x+8\right)$$

Use the distributive property to multiply 12+3x by x+8 and combine like terms.

$$P=36x+96+3x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3P+36}}{3}-6$$

$$x=-\frac{\sqrt{3P+36}}{3}-6$$

Solve for x

$$x=\frac{\sqrt{3P+36}}{3}-6$$

$$x=-\frac{\sqrt{3P+36}}{3}-6\text{, }P\geq -12$$