Solve (2x+3/4)(3/5x-9/3)

$$(2x+ \frac{ 3 }{ 4 } )( \frac{ 3 }{ 5 } x- \frac{ 9 }{ 3 } )$$

Evaluate

$$\frac{3\left(x-5\right)\left(8x+3\right)}{20}$$

Solution Steps

Divide 9 by 3 to get 3.

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

Apply the distributive property by multiplying each term of 2x+\frac{3}{4} by each term of \frac{3}{5}x-3.

$$2x\times \frac{3}{5}x-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

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

$$2x^{2}\times \frac{3}{5}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{2\times 3}{5}x^{2}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}x^{2}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Multiply \frac{3}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}x^{2}-6x+\frac{3\times 3}{4\times 5}x+\frac{3}{4}\left(-3\right)$$

Do the multiplications in the fraction \frac{3\times 3}{4\times 5}.

$$\frac{6}{5}x^{2}-6x+\frac{9}{20}x+\frac{3}{4}\left(-3\right)$$

Combine -6x and \frac{9}{20}x to get -\frac{111}{20}x.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{3}{4}\left(-3\right)$$

Express \frac{3}{4}\left(-3\right) as a single fraction.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{3\left(-3\right)}{4}$$

Multiply 3 and -3 to get -9.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{6}{5}x^{2}-\frac{111}{20}x-\frac{9}{4}$$

Expand

$$\frac{6x^{2}}{5}-\frac{111x}{20}-\frac{9}{4}$$

Solution Steps

Divide 9 by 3 to get 3.

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

Apply the distributive property by multiplying each term of 2x+\frac{3}{4} by each term of \frac{3}{5}x-3.

$$2x\times \frac{3}{5}x-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

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

$$2x^{2}\times \frac{3}{5}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{2\times 3}{5}x^{2}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}x^{2}-6x+\frac{3}{4}\times \frac{3}{5}x+\frac{3}{4}\left(-3\right)$$

Multiply \frac{3}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}x^{2}-6x+\frac{3\times 3}{4\times 5}x+\frac{3}{4}\left(-3\right)$$

Do the multiplications in the fraction \frac{3\times 3}{4\times 5}.

$$\frac{6}{5}x^{2}-6x+\frac{9}{20}x+\frac{3}{4}\left(-3\right)$$

Combine -6x and \frac{9}{20}x to get -\frac{111}{20}x.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{3}{4}\left(-3\right)$$

Express \frac{3}{4}\left(-3\right) as a single fraction.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{3\left(-3\right)}{4}$$

Multiply 3 and -3 to get -9.

$$\frac{6}{5}x^{2}-\frac{111}{20}x+\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{6}{5}x^{2}-\frac{111}{20}x-\frac{9}{4}$$