Solve for θ ( square root of 3tan(theta)-3)(8cos(x)+8)=0

$(\sqrt{3} \tan (θ) - 3) (8 \cos (x) + 8) = 0$

Simplify the left side.

Simplify $(\sqrt{3} \tan (θ) - 3) (8 \cos (x) + 8)$ .

Simplify each term.

Rewrite $\tan (θ)$ in terms of sines and cosines.

$(\sqrt{3} \frac{\sin (θ)}{\cos (θ)} - 3) (8 \cos (x) + 8) = 0$

Combine $\sqrt{3}$ and $\frac{\sin (θ)}{\cos (θ)}$ .

$(\frac{\sqrt{3} \sin (θ)}{\cos (θ)} - 3) (8 \cos (x) + 8) = 0$

Expand $(\frac{\sqrt{3} \sin (θ)}{\cos (θ)} - 3) (8 \cos (x) + 8)$ using the FOIL Method.

Apply the distributive property.

$\frac{\sqrt{3} \sin (θ)}{\cos (θ)} (8 \cos (x) + 8) - 3 (8 \cos (x) + 8) = 0$

Apply the distributive property.

$\frac{\sqrt{3} \sin (θ)}{\cos (θ)} (8 \cos (x)) + \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cdot 8 - 3 (8 \cos (x) + 8) = 0$

Apply the distributive property.

$\frac{\sqrt{3} \sin (θ)}{\cos (θ)} (8 \cos (x)) + \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cdot 8 - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cos (x) + \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cdot 8 - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Combine $8$ and $\frac{\sqrt{3} \sin (θ)}{\cos (θ)}$ .

$\frac{8 (\sqrt{3} \sin (θ))}{\cos (θ)} \cos (x) + \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cdot 8 - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Combine $\frac{8 \sqrt{3} \sin (θ)}{\cos (θ)}$ and $\cos (x)$ .

$\frac{8 \sqrt{3} \sin (θ) \cos (x)}{\cos (θ)} + \frac{\sqrt{3} \sin (θ)}{\cos (θ)} \cdot 8 - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Combine $\frac{\sqrt{3} \sin (θ)}{\cos (θ)}$ and $8$ .

$\frac{8 \sqrt{3} \sin (θ) \cos (x)}{\cos (θ)} + \frac{\sqrt{3} \sin (θ) \cdot 8}{\cos (θ)} - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Move $8$ to the left of $\sqrt{3} \sin (θ)$ .

$\frac{8 \sqrt{3} \sin (θ) \cos (x)}{\cos (θ)} + \frac{8 \cdot (\sqrt{3} \sin (θ))}{\cos (θ)} - 3 (8 \cos (x)) - 3 \cdot 8 = 0$

Multiply $8$ by $- 3$ .

$\frac{8 \sqrt{3} \sin (θ) \cos (x)}{\cos (θ)} + \frac{8 \sqrt{3} \sin (θ)}{\cos (θ)} - 24 \cos (x) - 3 \cdot 8 = 0$

Multiply $- 3$ by $8$ .

$\frac{8 \sqrt{3} \sin (θ) \cos (x)}{\cos (θ)} + \frac{8 \sqrt{3} \sin (θ)}{\cos (θ)} - 24 \cos (x) - 24 = 0$

Simplify each term.

Separate fractions.

$\frac{8 \sqrt{3} \cos (x)}{1} \cdot \frac{\sin (θ)}{\cos (θ)} + \frac{8 \sqrt{3} \sin (θ)}{\cos (θ)} - 24 \cos (x) - 24 = 0$

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\frac{8 \sqrt{3} \cos (x)}{1} \tan (θ) + \frac{8 \sqrt{3} \sin (θ)}{\cos (θ)} - 24 \cos (x) - 24 = 0$

Divide $8 \sqrt{3} \cos (x)$ by $1$ .

$8 \sqrt{3} \cos (x) \tan (θ) + \frac{8 \sqrt{3} \sin (θ)}{\cos (θ)} - 24 \cos (x) - 24 = 0$

Separate fractions.

$8 \sqrt{3} \cos (x) \tan (θ) + \frac{8 \sqrt{3}}{1} \cdot \frac{\sin (θ)}{\cos (θ)} - 24 \cos (x) - 24 = 0$

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$8 \sqrt{3} \cos (x) \tan (θ) + \frac{8 \sqrt{3}}{1} \tan (θ) - 24 \cos (x) - 24 = 0$

Divide $8 \sqrt{3}$ by $1$ .

$8 \sqrt{3} \cos (x) \tan (θ) + 8 \sqrt{3} \tan (θ) - 24 \cos (x) - 24 = 0$

Move all terms not containing $θ$ to the right side of the equation.

Add $24 \cos (x)$ to both sides of the equation.

$8 \sqrt{3} \cos (x) \tan (θ) + 8 \sqrt{3} \tan (θ) - 24 = 24 \cos (x)$

Add $24$ to both sides of the equation.

$8 \sqrt{3} \cos (x) \tan (θ) + 8 \sqrt{3} \tan (θ) = 24 \cos (x) + 24$

Solve for θ ( square root of 3tan(theta)-3)(8cos(x)+8)=0

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