Solve 24x-12/6-(x-9)(4x-5)=?

$$\frac { 24 x - 12 } { 6 } - ( x - 9 ) ( 4 x - 5 ) = ?$$

Evaluate

$$-4x^{2}+45x-47$$

Short Solution Steps

Apply the distributive property by multiplying each term of x-9 by each term of 4x-5.

$$\frac{24x-12}{6}-\left(4x^{2}-5x-36x+45\right)$$

Combine -5x and -36x to get -41x.

$$\frac{24x-12}{6}-\left(4x^{2}-41x+45\right)$$

To find the opposite of 4x^{2}-41x+45, find the opposite of each term.

$$\frac{24x-12}{6}-4x^{2}-\left(-41x\right)-45$$

The opposite of -41x is 41x.

$$\frac{24x-12}{6}-4x^{2}+41x-45$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4x^{2}+41x-45 times \frac{6}{6}.

$$\frac{24x-12}{6}+\frac{6\left(-4x^{2}+41x-45\right)}{6}$$

Since \frac{24x-12}{6} and \frac{6\left(-4x^{2}+41x-45\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{24x-12+6\left(-4x^{2}+41x-45\right)}{6}$$

Do the multiplications in 24x-12+6\left(-4x^{2}+41x-45\right).

$$\frac{24x-12-24x^{2}+246x-270}{6}$$

Combine like terms in 24x-12-24x^{2}+246x-270.

$$\frac{270x-282-24x^{2}}{6}$$

Divide each term of 270x-282-24x^{2} by 6 to get -47+45x-4x^{2}.

$$-47+45x-4x^{2}$$

Expand

$$-4x^{2}+45x-47$$

Short Solution Steps

Apply the distributive property by multiplying each term of x-9 by each term of 4x-5.

$$\frac{24x-12}{6}-\left(4x^{2}-5x-36x+45\right)$$

Combine -5x and -36x to get -41x.

$$\frac{24x-12}{6}-\left(4x^{2}-41x+45\right)$$

To find the opposite of 4x^{2}-41x+45, find the opposite of each term.

$$\frac{24x-12}{6}-4x^{2}-\left(-41x\right)-45$$

The opposite of -41x is 41x.

$$\frac{24x-12}{6}-4x^{2}+41x-45$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4x^{2}+41x-45 times \frac{6}{6}.

$$\frac{24x-12}{6}+\frac{6\left(-4x^{2}+41x-45\right)}{6}$$

Since \frac{24x-12}{6} and \frac{6\left(-4x^{2}+41x-45\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{24x-12+6\left(-4x^{2}+41x-45\right)}{6}$$

Do the multiplications in 24x-12+6\left(-4x^{2}+41x-45\right).

$$\frac{24x-12-24x^{2}+246x-270}{6}$$

Combine like terms in 24x-12-24x^{2}+246x-270.

$$\frac{270x-282-24x^{2}}{6}$$

Divide each term of 270x-282-24x^{2} by 6 to get -47+45x-4x^{2}.

$$-47+45x-4x^{2}$$