Solve C=(6x+9)(6x-9)

$$C = ( 6 x + 9 ) ( 6 x - 9 )$$

Solve for C

$$C=36x^{2}-81$$

Solution Steps

Consider \left(6x+9\right)\left(6x-9\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 9.

$$C=\left(6x\right)^{2}-81$$

Expand \left(6x\right)^{2}.

$$C=6^{2}x^{2}-81$$

Calculate 6 to the power of 2 and get 36.

$$C=36x^{2}-81$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{C+81}}{6}$$

$$x=\frac{\sqrt{C+81}}{6}$$

Solve for x

$$x=-\frac{\sqrt{C+81}}{6}$$

$$x=\frac{\sqrt{C+81}}{6}\text{, }C\geq -81$$