Solve for x 2x square root of 7=6 square root of 63

$2 x \sqrt{7} = 6 \sqrt{63}$

Simplify.

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$2 x \sqrt{7} = 6 \sqrt{9 (7)}$

Rewrite $9$ as $3^{2}$ .

$2 x \sqrt{7} = 6 \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$2 x \sqrt{7} = 6 (3 \sqrt{7})$

Multiply $3$ by $6$ .

$2 x \sqrt{7} = 18 \sqrt{7}$

Divide each term in $2 x \sqrt{7} = 18 \sqrt{7}$ by $2 \sqrt{7}$ and simplify.

Divide each term in $2 x \sqrt{7} = 18 \sqrt{7}$ by $2 \sqrt{7}$ .

$\frac{2 x \sqrt{7}}{2 \sqrt{7}} = \frac{18 \sqrt{7}}{2 \sqrt{7}}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \sqrt{7}}{2 \sqrt{7}} = \frac{18 \sqrt{7}}{2 \sqrt{7}}$

Rewrite the expression.

$\frac{x \sqrt{7}}{\sqrt{7}} = \frac{18 \sqrt{7}}{2 \sqrt{7}}$

Cancel the common factor of $\sqrt{7}$ .

Cancel the common factor.

$\frac{x \sqrt{7}}{\sqrt{7}} = \frac{18 \sqrt{7}}{2 \sqrt{7}}$

Divide $x$ by $1$ .

$x = \frac{18 \sqrt{7}}{2 \sqrt{7}}$

Simplify the right side.

Cancel the common factor of $18$ and $2$ .

Factor $2$ out of $18 \sqrt{7}$ .

$x = \frac{2 (9 \sqrt{7})}{2 \sqrt{7}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt{7}$ .

$x = \frac{2 (9 \sqrt{7})}{2 (\sqrt{7})}$

Cancel the common factor.

$x = \frac{2 (9 \sqrt{7})}{2 \sqrt{7}}$

Rewrite the expression.

$x = \frac{9 \sqrt{7}}{\sqrt{7}}$

Cancel the common factor of $\sqrt{7}$ .

Cancel the common factor.

$x = \frac{9 \sqrt{7}}{\sqrt{7}}$

Divide $9$ by $1$ .

$x = 9$