Solve for x -2 cube root of 16x-3 cube root of 54x=39

$- 2 \sqrt[3]{16 x} - 3 \sqrt[3]{54 x} = 39$

Simplify $- 2 \sqrt[3]{16 x} - 3 \sqrt[3]{54 x}$ .

Simplify each term.

Rewrite $16 x$ as $2^{3} \cdot (2 x)$ .

Factor $8$ out of $16$ .

$- 2 \sqrt[3]{8 (2) x} - 3 \sqrt[3]{54 x} = 39$

Rewrite $8$ as $2^{3}$ .

$- 2 \sqrt[3]{2^{3} \cdot 2 x} - 3 \sqrt[3]{54 x} = 39$

Add parentheses.

$- 2 \sqrt[3]{2^{3} \cdot (2 x)} - 3 \sqrt[3]{54 x} = 39$

Pull terms out from under the radical.

$- 2 (2 \sqrt[3]{2 x}) - 3 \sqrt[3]{54 x} = 39$

Multiply $2$ by $- 2$ .

$- 4 \sqrt[3]{2 x} - 3 \sqrt[3]{54 x} = 39$

Rewrite $54 x$ as $3^{3} \cdot (2 x)$ .

Factor $27$ out of $54$ .

$- 4 \sqrt[3]{2 x} - 3 \sqrt[3]{27 (2) x} = 39$

Rewrite $27$ as $3^{3}$ .

$- 4 \sqrt[3]{2 x} - 3 \sqrt[3]{3^{3} \cdot 2 x} = 39$

Add parentheses.

$- 4 \sqrt[3]{2 x} - 3 \sqrt[3]{3^{3} \cdot (2 x)} = 39$

Pull terms out from under the radical.

$- 4 \sqrt[3]{2 x} - 3 (3 \sqrt[3]{2 x}) = 39$

Multiply $3$ by $- 3$ .

$- 4 \sqrt[3]{2 x} - 9 \sqrt[3]{2 x} = 39$

Subtract $9 \sqrt[3]{2 x}$ from $- 4 \sqrt[3]{2 x}$ .

$- 13 \sqrt[3]{2 x} = 39$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - \frac{27}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{27}{2}$

Decimal Form:

$x = - 13.5$

Mixed Number Form:

$x = - 13 \frac{1}{2}$