Solve (x/5)*(2/3-2x)

$$( \frac { x } { 5 } ) \cdot ( \frac { 2 } { 3 } - 2 x )$$

Evaluate

$$\frac{2x\left(1-3x\right)}{15}$$

Short Solution Steps

Use the distributive property to multiply \frac{x}{5} by \frac{2}{3}-2x.

$$\frac{x}{5}\times \frac{2}{3}-2\times \frac{x}{5}x$$

Multiply \frac{x}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\times 2}{5\times 3}-2\times \frac{x}{5}x$$

Express -2\times \frac{x}{5} as a single fraction.

$$\frac{x\times 2}{5\times 3}+\frac{-2x}{5}x$$

Express \frac{-2x}{5}x as a single fraction.

$$\frac{x\times 2}{5\times 3}+\frac{-2xx}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 3 and 5 is 3\times 5. Multiply \frac{-2xx}{5} times \frac{3}{3}.

$$\frac{x\times 2}{3\times 5}+\frac{3\left(-1\right)\times 2xx}{3\times 5}$$

Since \frac{x\times 2}{3\times 5} and \frac{3\left(-1\right)\times 2xx}{3\times 5} have the same denominator, add them by adding their numerators.

$$\frac{x\times 2+3\left(-1\right)\times 2xx}{3\times 5}$$

Do the multiplications in x\times 2+3\left(-1\right)\times 2xx.

$$\frac{x\times 2-6x^{2}}{3\times 5}$$

Expand 3\times 5.

$$\frac{x\times 2-6x^{2}}{15}$$

Expand

$$-\frac{2x^{2}}{5}+\frac{2x}{15}$$

Short Solution Steps

Use the distributive property to multiply \frac{x}{5} by \frac{2}{3}-2x.

$$\frac{x}{5}\times \frac{2}{3}-2\times \frac{x}{5}x$$

Multiply \frac{x}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\times 2}{5\times 3}-2\times \frac{x}{5}x$$

Express -2\times \frac{x}{5} as a single fraction.

$$\frac{x\times 2}{5\times 3}+\frac{-2x}{5}x$$

Express \frac{-2x}{5}x as a single fraction.

$$\frac{x\times 2}{5\times 3}+\frac{-2xx}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 3 and 5 is 3\times 5. Multiply \frac{-2xx}{5} times \frac{3}{3}.

$$\frac{x\times 2}{3\times 5}+\frac{3\left(-1\right)\times 2xx}{3\times 5}$$

Since \frac{x\times 2}{3\times 5} and \frac{3\left(-1\right)\times 2xx}{3\times 5} have the same denominator, add them by adding their numerators.

$$\frac{x\times 2+3\left(-1\right)\times 2xx}{3\times 5}$$

Do the multiplications in x\times 2+3\left(-1\right)\times 2xx.

$$\frac{x\times 2-6x^{2}}{3\times 5}$$

Expand 3\times 5.

$$\frac{x\times 2-6x^{2}}{15}$$