Solve (x+5)(x-123/6)=

$$( x + 5 ) ( x - \frac { 123 } { 6 } ) =$$

Evaluate

$$x^{2}-\frac{31x}{2}-\frac{205}{2}$$

Solution Steps

Reduce the fraction \frac{123}{6} to lowest terms by extracting and canceling out 3.

$$\left(x+5\right)\left(x-\frac{41}{2}\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of x-\frac{41}{2}.

$$x^{2}+x\left(-\frac{41}{2}\right)+5x+5\left(-\frac{41}{2}\right)$$

Combine x\left(-\frac{41}{2}\right) and 5x to get -\frac{31}{2}x.

$$x^{2}-\frac{31}{2}x+5\left(-\frac{41}{2}\right)$$

Express 5\left(-\frac{41}{2}\right) as a single fraction.

$$x^{2}-\frac{31}{2}x+\frac{5\left(-41\right)}{2}$$

Multiply 5 and -41 to get -205.

$$x^{2}-\frac{31}{2}x+\frac{-205}{2}$$

Fraction \frac{-205}{2} can be rewritten as -\frac{205}{2} by extracting the negative sign.

$$x^{2}-\frac{31}{2}x-\frac{205}{2}$$

Expand

$$x^{2}-\frac{31x}{2}-\frac{205}{2}$$

Solution Steps

Reduce the fraction \frac{123}{6} to lowest terms by extracting and canceling out 3.

$$\left(x+5\right)\left(x-\frac{41}{2}\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of x-\frac{41}{2}.

$$x^{2}+x\left(-\frac{41}{2}\right)+5x+5\left(-\frac{41}{2}\right)$$

Combine x\left(-\frac{41}{2}\right) and 5x to get -\frac{31}{2}x.

$$x^{2}-\frac{31}{2}x+5\left(-\frac{41}{2}\right)$$

Express 5\left(-\frac{41}{2}\right) as a single fraction.

$$x^{2}-\frac{31}{2}x+\frac{5\left(-41\right)}{2}$$

Multiply 5 and -41 to get -205.

$$x^{2}-\frac{31}{2}x+\frac{-205}{2}$$

Fraction \frac{-205}{2} can be rewritten as -\frac{205}{2} by extracting the negative sign.

$$x^{2}-\frac{31}{2}x-\frac{205}{2}$$