Solve sqrt{12}(sqrt{3}-x)=15

$$\sqrt { 12 } ( \sqrt { 3 } - x ) = 15$$

Solve for x

$$x = -\frac{3 \sqrt{3}}{2} \approx -2.598076211$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}\left(\sqrt{3}-x\right)=15$$

Use the distributive property to multiply 2\sqrt{3} by \sqrt{3}-x.

$$2\left(\sqrt{3}\right)^{2}-2\sqrt{3}x=15$$

The square of \sqrt{3} is 3.

$$2\times 3-2\sqrt{3}x=15$$

Multiply 2 and 3 to get 6.

$$6-2\sqrt{3}x=15$$

Subtract 6 from both sides.

$$-2\sqrt{3}x=15-6$$

Subtract 6 from 15 to get 9.

$$-2\sqrt{3}x=9$$

The equation is in standard form.

$$\left(-2\sqrt{3}\right)x=9$$

Divide both sides by -2\sqrt{3}.

$$\frac{\left(-2\sqrt{3}\right)x}{-2\sqrt{3}}=\frac{9}{-2\sqrt{3}}$$

Dividing by -2\sqrt{3} undoes the multiplication by -2\sqrt{3}.

$$x=\frac{9}{-2\sqrt{3}}$$

Divide 9 by -2\sqrt{3}.

$$x=-\frac{3\sqrt{3}}{2}$$