Solve (x+6+x-3/2)(x-3+x+5)

$$( x + 6 + \frac { x - 3 } { 2 } ) ( x - 3 + x + 5 )$$

Evaluate

$$3\left(x+1\right)\left(x+3\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+6 times \frac{2}{2}.

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

Since \frac{2\left(x+6\right)}{2} and \frac{x-3}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x+6\right)+x-3.

$$\frac{2x+12+x-3}{2}\left(x-3+x+5\right)$$

Combine like terms in 2x+12+x-3.

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

Combine x and x to get 2x.

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

Add -3 and 5 to get 2.

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

Express \frac{3x+9}{2}\left(2x+2\right) as a single fraction.

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

Apply the distributive property by multiplying each term of 3x+9 by each term of 2x+2.

$$\frac{6x^{2}+6x+18x+18}{2}$$

Combine 6x and 18x to get 24x.

$$\frac{6x^{2}+24x+18}{2}$$

Expand

$$3x^{2}+12x+9$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x+6 times \frac{2}{2}.

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

Since \frac{2\left(x+6\right)}{2} and \frac{x-3}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x+6\right)+x-3.

$$\frac{2x+12+x-3}{2}\left(x-3+x+5\right)$$

Combine like terms in 2x+12+x-3.

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

Combine x and x to get 2x.

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

Add -3 and 5 to get 2.

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

Express \frac{3x+9}{2}\left(2x+2\right) as a single fraction.

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

Apply the distributive property by multiplying each term of 3x+9 by each term of 2x+2.

$$\frac{6x^{2}+6x+18x+18}{2}$$

Combine 6x and 18x to get 24x.

$$\frac{6x^{2}+24x+18}{2}$$