Solve 5(6x-1/2)(x-2)-3

$$5 ( 6 x - \frac { 1 } { 2 } ) ( x - 2 ) - 3$$

Evaluate

$$30x^{2}-\frac{125x}{2}+2$$

Solution Steps

Use the distributive property to multiply 5 by 6x-\frac{1}{2}.

$$\left(30x+5\left(-\frac{1}{2}\right)\right)\left(x-2\right)-3$$

Express 5\left(-\frac{1}{2}\right) as a single fraction.

$$\left(30x+\frac{5\left(-1\right)}{2}\right)\left(x-2\right)-3$$

Multiply 5 and -1 to get -5.

$$\left(30x+\frac{-5}{2}\right)\left(x-2\right)-3$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\left(30x-\frac{5}{2}\right)\left(x-2\right)-3$$

Apply the distributive property by multiplying each term of 30x-\frac{5}{2} by each term of x-2.

$$30x^{2}-60x-\frac{5}{2}x-\frac{5}{2}\left(-2\right)-3$$

Combine -60x and -\frac{5}{2}x to get -\frac{125}{2}x.

$$30x^{2}-\frac{125}{2}x-\frac{5}{2}\left(-2\right)-3$$

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

$$30x^{2}-\frac{125}{2}x+\frac{-5\left(-2\right)}{2}-3$$

Multiply -5 and -2 to get 10.

$$30x^{2}-\frac{125}{2}x+\frac{10}{2}-3$$

Divide 10 by 2 to get 5.

$$30x^{2}-\frac{125}{2}x+5-3$$

Subtract 3 from 5 to get 2.

$$30x^{2}-\frac{125}{2}x+2$$

Expand

$$30x^{2}-\frac{125x}{2}+2$$

Solution Steps

Use the distributive property to multiply 5 by 6x-\frac{1}{2}.

$$\left(30x+5\left(-\frac{1}{2}\right)\right)\left(x-2\right)-3$$

Express 5\left(-\frac{1}{2}\right) as a single fraction.

$$\left(30x+\frac{5\left(-1\right)}{2}\right)\left(x-2\right)-3$$

Multiply 5 and -1 to get -5.

$$\left(30x+\frac{-5}{2}\right)\left(x-2\right)-3$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\left(30x-\frac{5}{2}\right)\left(x-2\right)-3$$

Apply the distributive property by multiplying each term of 30x-\frac{5}{2} by each term of x-2.

$$30x^{2}-60x-\frac{5}{2}x-\frac{5}{2}\left(-2\right)-3$$

Combine -60x and -\frac{5}{2}x to get -\frac{125}{2}x.

$$30x^{2}-\frac{125}{2}x-\frac{5}{2}\left(-2\right)-3$$

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

$$30x^{2}-\frac{125}{2}x+\frac{-5\left(-2\right)}{2}-3$$

Multiply -5 and -2 to get 10.

$$30x^{2}-\frac{125}{2}x+\frac{10}{2}-3$$

Divide 10 by 2 to get 5.

$$30x^{2}-\frac{125}{2}x+5-3$$

Subtract 3 from 5 to get 2.

$$30x^{2}-\frac{125}{2}x+2$$