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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

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

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2-x.

$$\frac{6-x}{2}\left(2x+9\right)$$

Express \frac{6-x}{2}\left(2x+9\right) as a single fraction.

$$\frac{\left(6-x\right)\left(2x+9\right)}{2}$$

Apply the distributive property by multiplying each term of 6-x by each term of 2x+9.

$$\frac{12x+54-2x^{2}-9x}{2}$$

Combine 12x and -9x to get 3x.

$$\frac{3x+54-2x^{2}}{2}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

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

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2-x.

$$\frac{6-x}{2}\left(2x+9\right)$$

Express \frac{6-x}{2}\left(2x+9\right) as a single fraction.

$$\frac{\left(6-x\right)\left(2x+9\right)}{2}$$

Apply the distributive property by multiplying each term of 6-x by each term of 2x+9.

$$\frac{12x+54-2x^{2}-9x}{2}$$

Combine 12x and -9x to get 3x.

$$\frac{3x+54-2x^{2}}{2}$$