Solve 5x^2/2+35x/2+24+(x(x+9)/2)

$$\frac { 5 x ^ { 2 } } { 2 } + \frac { 35 x } { 2 } + 24 + ( \frac { x ( x + 9 ) } { 2 } )$$

Evaluate

$$\left(x+6\right)\left(3x+4\right)$$

Short Solution Steps

Since \frac{5x^{2}}{2} and \frac{35x}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x}{2}+24+\frac{x\left(x+9\right)}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 24 times \frac{2}{2}.

$$\frac{5x^{2}+35x}{2}+\frac{24\times 2}{2}+\frac{x\left(x+9\right)}{2}$$

Since \frac{5x^{2}+35x}{2} and \frac{24\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x+24\times 2}{2}+\frac{x\left(x+9\right)}{2}$$

Do the multiplications in 5x^{2}+35x+24\times 2.

$$\frac{5x^{2}+35x+48}{2}+\frac{x\left(x+9\right)}{2}$$

Since \frac{5x^{2}+35x+48}{2} and \frac{x\left(x+9\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x+48+x\left(x+9\right)}{2}$$

Do the multiplications in 5x^{2}+35x+48+x\left(x+9\right).

$$\frac{5x^{2}+35x+48+x^{2}+9x}{2}$$

Combine like terms in 5x^{2}+35x+48+x^{2}+9x.

$$\frac{6x^{2}+44x+48}{2}$$

Divide each term of 6x^{2}+44x+48 by 2 to get 24+22x+3x^{2}.

$$24+22x+3x^{2}$$

Expand

$$3x^{2}+22x+24$$

Short Solution Steps

Since \frac{5x^{2}}{2} and \frac{35x}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x}{2}+24+\frac{x\left(x+9\right)}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 24 times \frac{2}{2}.

$$\frac{5x^{2}+35x}{2}+\frac{24\times 2}{2}+\frac{x\left(x+9\right)}{2}$$

Since \frac{5x^{2}+35x}{2} and \frac{24\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x+24\times 2}{2}+\frac{x\left(x+9\right)}{2}$$

Do the multiplications in 5x^{2}+35x+24\times 2.

$$\frac{5x^{2}+35x+48}{2}+\frac{x\left(x+9\right)}{2}$$

Since \frac{5x^{2}+35x+48}{2} and \frac{x\left(x+9\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{5x^{2}+35x+48+x\left(x+9\right)}{2}$$

Do the multiplications in 5x^{2}+35x+48+x\left(x+9\right).

$$\frac{5x^{2}+35x+48+x^{2}+9x}{2}$$

Combine like terms in 5x^{2}+35x+48+x^{2}+9x.

$$\frac{6x^{2}+44x+48}{2}$$

Divide each term of 6x^{2}+44x+48 by 2 to get 24+22x+3x^{2}.

$$24+22x+3x^{2}$$