Solve -3/8(x+5)(x-3)

$$- \frac{ 3 }{ 8 } (x+5)(x-3)$$

Evaluate

$$-\frac{3\left(x-3\right)\left(x+5\right)}{8}$$

Solution Steps

Use the distributive property to multiply -\frac{3}{8} by x+5.

$$\left(-\frac{3}{8}x-\frac{3}{8}\times 5\right)\left(x-3\right)$$

Express -\frac{3}{8}\times 5 as a single fraction.

$$\left(-\frac{3}{8}x+\frac{-3\times 5}{8}\right)\left(x-3\right)$$

Multiply -3 and 5 to get -15.

$$\left(-\frac{3}{8}x+\frac{-15}{8}\right)\left(x-3\right)$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\left(-\frac{3}{8}x-\frac{15}{8}\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -\frac{3}{8}x-\frac{15}{8} by each term of x-3.

$$-\frac{3}{8}xx-\frac{3}{8}x\left(-3\right)-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

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

$$-\frac{3}{8}x^{2}-\frac{3}{8}x\left(-3\right)-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Express -\frac{3}{8}\left(-3\right) as a single fraction.

$$-\frac{3}{8}x^{2}+\frac{-3\left(-3\right)}{8}x-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Multiply -3 and -3 to get 9.

$$-\frac{3}{8}x^{2}+\frac{9}{8}x-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Combine \frac{9}{8}x and -\frac{15}{8}x to get -\frac{3}{4}x.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x-\frac{15}{8}\left(-3\right)$$

Express -\frac{15}{8}\left(-3\right) as a single fraction.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x+\frac{-15\left(-3\right)}{8}$$

Multiply -15 and -3 to get 45.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x+\frac{45}{8}$$

Expand

$$-\frac{3x^{2}}{8}-\frac{3x}{4}+\frac{45}{8}$$

Solution Steps

Use the distributive property to multiply -\frac{3}{8} by x+5.

$$\left(-\frac{3}{8}x-\frac{3}{8}\times 5\right)\left(x-3\right)$$

Express -\frac{3}{8}\times 5 as a single fraction.

$$\left(-\frac{3}{8}x+\frac{-3\times 5}{8}\right)\left(x-3\right)$$

Multiply -3 and 5 to get -15.

$$\left(-\frac{3}{8}x+\frac{-15}{8}\right)\left(x-3\right)$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\left(-\frac{3}{8}x-\frac{15}{8}\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -\frac{3}{8}x-\frac{15}{8} by each term of x-3.

$$-\frac{3}{8}xx-\frac{3}{8}x\left(-3\right)-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

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

$$-\frac{3}{8}x^{2}-\frac{3}{8}x\left(-3\right)-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Express -\frac{3}{8}\left(-3\right) as a single fraction.

$$-\frac{3}{8}x^{2}+\frac{-3\left(-3\right)}{8}x-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Multiply -3 and -3 to get 9.

$$-\frac{3}{8}x^{2}+\frac{9}{8}x-\frac{15}{8}x-\frac{15}{8}\left(-3\right)$$

Combine \frac{9}{8}x and -\frac{15}{8}x to get -\frac{3}{4}x.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x-\frac{15}{8}\left(-3\right)$$

Express -\frac{15}{8}\left(-3\right) as a single fraction.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x+\frac{-15\left(-3\right)}{8}$$

Multiply -15 and -3 to get 45.

$$-\frac{3}{8}x^{2}-\frac{3}{4}x+\frac{45}{8}$$