Solve (x/4-1/2)(-2/3x+4/5)

$$( \frac{ x }{ 4 } - \frac{ 1 }{ 2 } )(- \frac{ 2 }{ 3 } x+ \frac{ 4 }{ 5 } )$$

Evaluate

$$\frac{\left(6-5x\right)\left(x-2\right)}{30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\left(\frac{x}{4}-\frac{2}{4}\right)\left(-\frac{2}{3}x+\frac{4}{5}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-2}{4}\left(-\frac{2}{3}x+\frac{4}{5}\right)$$

Use the distributive property to multiply \frac{x-2}{4} by -\frac{2}{3}x+\frac{4}{5}.

$$\frac{x-2}{4}\left(-\frac{2}{3}\right)x+\frac{x-2}{4}\times \frac{4}{5}$$

Multiply \frac{x-2}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(x-2\right)\times 2}{4\times 3}x+\frac{x-2}{4}\times \frac{4}{5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(x-2\right)}{2\times 3}x+\frac{x-2}{4}\times \frac{4}{5}$$

Express \frac{-\left(x-2\right)}{2\times 3}x as a single fraction.

$$\frac{-\left(x-2\right)x}{2\times 3}+\frac{x-2}{4}\times \frac{4}{5}$$

Multiply \frac{x-2}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(x-2\right)x}{2\times 3}+\frac{\left(x-2\right)\times 4}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 3 and 5 is 30. Multiply \frac{-\left(x-2\right)x}{2\times 3} times \frac{5}{5}. Multiply \frac{x-2}{5} times \frac{6}{6}.

$$\frac{5\left(-1\right)\left(x-2\right)x}{30}+\frac{6\left(x-2\right)}{30}$$

Since \frac{5\left(-1\right)\left(x-2\right)x}{30} and \frac{6\left(x-2\right)}{30} have the same denominator, add them by adding their numerators.

$$\frac{5\left(-1\right)\left(x-2\right)x+6\left(x-2\right)}{30}$$

Do the multiplications in 5\left(-1\right)\left(x-2\right)x+6\left(x-2\right).

$$\frac{-5x^{2}+10x+6x-12}{30}$$

Combine like terms in -5x^{2}+10x+6x-12.

$$\frac{-5x^{2}+16x-12}{30}$$

Expand

$$-\frac{x^{2}}{6}+\frac{8x}{15}-\frac{2}{5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\left(\frac{x}{4}-\frac{2}{4}\right)\left(-\frac{2}{3}x+\frac{4}{5}\right)$$

Since \frac{x}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-2}{4}\left(-\frac{2}{3}x+\frac{4}{5}\right)$$

Use the distributive property to multiply \frac{x-2}{4} by -\frac{2}{3}x+\frac{4}{5}.

$$\frac{x-2}{4}\left(-\frac{2}{3}\right)x+\frac{x-2}{4}\times \frac{4}{5}$$

Multiply \frac{x-2}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(x-2\right)\times 2}{4\times 3}x+\frac{x-2}{4}\times \frac{4}{5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(x-2\right)}{2\times 3}x+\frac{x-2}{4}\times \frac{4}{5}$$

Express \frac{-\left(x-2\right)}{2\times 3}x as a single fraction.

$$\frac{-\left(x-2\right)x}{2\times 3}+\frac{x-2}{4}\times \frac{4}{5}$$

Multiply \frac{x-2}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(x-2\right)x}{2\times 3}+\frac{\left(x-2\right)\times 4}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 3 and 5 is 30. Multiply \frac{-\left(x-2\right)x}{2\times 3} times \frac{5}{5}. Multiply \frac{x-2}{5} times \frac{6}{6}.

$$\frac{5\left(-1\right)\left(x-2\right)x}{30}+\frac{6\left(x-2\right)}{30}$$

Since \frac{5\left(-1\right)\left(x-2\right)x}{30} and \frac{6\left(x-2\right)}{30} have the same denominator, add them by adding their numerators.

$$\frac{5\left(-1\right)\left(x-2\right)x+6\left(x-2\right)}{30}$$

Do the multiplications in 5\left(-1\right)\left(x-2\right)x+6\left(x-2\right).

$$\frac{-5x^{2}+10x+6x-12}{30}$$

Combine like terms in -5x^{2}+10x+6x-12.

$$\frac{-5x^{2}+16x-12}{30}$$