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

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

Evaluate

$$\frac{3\left(4-3x\right)\left(x+3\right)}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of 2-\frac{3}{2}x by each term of \frac{3}{4}x+\frac{9}{4}.

$$2\times \frac{3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x\times \frac{3}{4}x-\frac{3}{2}x\times \frac{9}{4}$$

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

$$2\times \frac{3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Express 2\times \frac{9}{4} as a single fraction.

$$\frac{3}{2}x+\frac{2\times 9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply 2 and 9 to get 18.

$$\frac{3}{2}x+\frac{18}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x+\frac{9}{2}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

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

$$\frac{3}{2}x+\frac{9}{2}+\frac{-3\times 3}{2\times 4}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Do the multiplications in the fraction \frac{-3\times 3}{2\times 4}.

$$\frac{3}{2}x+\frac{9}{2}+\frac{-9}{8}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply -\frac{3}{2} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}+\frac{-3\times 9}{2\times 4}x$$

Do the multiplications in the fraction \frac{-3\times 9}{2\times 4}.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}+\frac{-27}{8}x$$

Fraction \frac{-27}{8} can be rewritten as -\frac{27}{8} by extracting the negative sign.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}-\frac{27}{8}x$$

Combine \frac{3}{2}x and -\frac{27}{8}x to get -\frac{15}{8}x.

$$-\frac{15}{8}x+\frac{9}{2}-\frac{9}{8}x^{2}$$

Expand

$$-\frac{9x^{2}}{8}-\frac{15x}{8}+\frac{9}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2-\frac{3}{2}x by each term of \frac{3}{4}x+\frac{9}{4}.

$$2\times \frac{3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x\times \frac{3}{4}x-\frac{3}{2}x\times \frac{9}{4}$$

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

$$2\times \frac{3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{2\times 3}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{4}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x+2\times \frac{9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Express 2\times \frac{9}{4} as a single fraction.

$$\frac{3}{2}x+\frac{2\times 9}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply 2 and 9 to get 18.

$$\frac{3}{2}x+\frac{18}{4}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x+\frac{9}{2}-\frac{3}{2}x^{2}\times \frac{3}{4}-\frac{3}{2}x\times \frac{9}{4}$$

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

$$\frac{3}{2}x+\frac{9}{2}+\frac{-3\times 3}{2\times 4}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Do the multiplications in the fraction \frac{-3\times 3}{2\times 4}.

$$\frac{3}{2}x+\frac{9}{2}+\frac{-9}{8}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}-\frac{3}{2}x\times \frac{9}{4}$$

Multiply -\frac{3}{2} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}+\frac{-3\times 9}{2\times 4}x$$

Do the multiplications in the fraction \frac{-3\times 9}{2\times 4}.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}+\frac{-27}{8}x$$

Fraction \frac{-27}{8} can be rewritten as -\frac{27}{8} by extracting the negative sign.

$$\frac{3}{2}x+\frac{9}{2}-\frac{9}{8}x^{2}-\frac{27}{8}x$$

Combine \frac{3}{2}x and -\frac{27}{8}x to get -\frac{15}{8}x.

$$-\frac{15}{8}x+\frac{9}{2}-\frac{9}{8}x^{2}$$