Solve (x-30)(74/25x-459/5)

$$( x - 30 ) ( \frac { 74 } { 25 } x - \frac { 459 } { 5 } )$$

Evaluate

$$\frac{\left(x-30\right)\left(74x-2295\right)}{25}$$

Solution Steps

Apply the distributive property by multiplying each term of x-30 by each term of \frac{74}{25}x-\frac{459}{5}.

$$x\times \frac{74}{25}x+x\left(-\frac{459}{5}\right)-30\times \frac{74}{25}x-30\left(-\frac{459}{5}\right)$$

Multiply x and x to get x^{2}.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)-30\times \frac{74}{25}x-30\left(-\frac{459}{5}\right)$$

Express -30\times \frac{74}{25} as a single fraction.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)+\frac{-30\times 74}{25}x-30\left(-\frac{459}{5}\right)$$

Multiply -30 and 74 to get -2220.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)+\frac{-2220}{25}x-30\left(-\frac{459}{5}\right)$$

Reduce the fraction \frac{-2220}{25} to lowest terms by extracting and canceling out 5.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)-\frac{444}{5}x-30\left(-\frac{459}{5}\right)$$

Combine x\left(-\frac{459}{5}\right) and -\frac{444}{5}x to get -\frac{903}{5}x.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x-30\left(-\frac{459}{5}\right)$$

Express -30\left(-\frac{459}{5}\right) as a single fraction.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+\frac{-30\left(-459\right)}{5}$$

Multiply -30 and -459 to get 13770.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+\frac{13770}{5}$$

Divide 13770 by 5 to get 2754.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+2754$$

Expand

$$\frac{74x^{2}}{25}-\frac{903x}{5}+2754$$

Solution Steps

Apply the distributive property by multiplying each term of x-30 by each term of \frac{74}{25}x-\frac{459}{5}.

$$x\times \frac{74}{25}x+x\left(-\frac{459}{5}\right)-30\times \frac{74}{25}x-30\left(-\frac{459}{5}\right)$$

Multiply x and x to get x^{2}.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)-30\times \frac{74}{25}x-30\left(-\frac{459}{5}\right)$$

Express -30\times \frac{74}{25} as a single fraction.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)+\frac{-30\times 74}{25}x-30\left(-\frac{459}{5}\right)$$

Multiply -30 and 74 to get -2220.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)+\frac{-2220}{25}x-30\left(-\frac{459}{5}\right)$$

Reduce the fraction \frac{-2220}{25} to lowest terms by extracting and canceling out 5.

$$x^{2}\times \frac{74}{25}+x\left(-\frac{459}{5}\right)-\frac{444}{5}x-30\left(-\frac{459}{5}\right)$$

Combine x\left(-\frac{459}{5}\right) and -\frac{444}{5}x to get -\frac{903}{5}x.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x-30\left(-\frac{459}{5}\right)$$

Express -30\left(-\frac{459}{5}\right) as a single fraction.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+\frac{-30\left(-459\right)}{5}$$

Multiply -30 and -459 to get 13770.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+\frac{13770}{5}$$

Divide 13770 by 5 to get 2754.

$$x^{2}\times \frac{74}{25}-\frac{903}{5}x+2754$$