Solve -(x+frac{3sqrt{2}}{2})(3x+frac{sqrt{2}}{2})

$$-(x+ \frac{ 3 \sqrt{ 2 } }{ 2 } )(3x+ \frac{ \sqrt{ 2 } }{ 2 } )$$

Evaluate

$$-3x^{2}-5\sqrt{2}x-\frac{3}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2}{2}.

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

Since \frac{2x}{2} and \frac{3\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

$$\left(-\frac{2x+3\sqrt{2}}{2}\right)\left(\frac{2\times 3x}{2}+\frac{\sqrt{2}}{2}\right)$$

Since \frac{2\times 3x}{2} and \frac{\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\left(-\frac{2x+3\sqrt{2}}{2}\right)\times \frac{2\times 3x+\sqrt{2}}{2}$$

Do the multiplications in 2\times 3x+\sqrt{2}.

$$\left(-\frac{2x+3\sqrt{2}}{2}\right)\times \frac{6x+\sqrt{2}}{2}$$

Multiply -\frac{2x+3\sqrt{2}}{2} times \frac{6x+\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(2x+3\sqrt{2}\right)\left(6x+\sqrt{2}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-\left(2x+3\sqrt{2}\right)\left(6x+\sqrt{2}\right)}{4}$$

Use the distributive property to multiply -1 by 2x+3\sqrt{2}.

$$\frac{\left(-2x-3\sqrt{2}\right)\left(6x+\sqrt{2}\right)}{4}$$

Apply the distributive property by multiplying each term of -2x-3\sqrt{2} by each term of 6x+\sqrt{2}.

$$\frac{-12x^{2}-2x\sqrt{2}-18x\sqrt{2}-3\left(\sqrt{2}\right)^{2}}{4}$$

Combine -2x\sqrt{2} and -18x\sqrt{2} to get -20x\sqrt{2}.

$$\frac{-12x^{2}-20x\sqrt{2}-3\left(\sqrt{2}\right)^{2}}{4}$$

The square of \sqrt{2} is 2.

$$\frac{-12x^{2}-20x\sqrt{2}-3\times 2}{4}$$

Multiply -3 and 2 to get -6.

$$\frac{-12x^{2}-20x\sqrt{2}-6}{4}$$

Factor

$$\frac{-6x^{2}-10\sqrt{2}x-3}{2}$$