Solve 180(120-3/5x)x+60(12000-(120-3/5x)x)

$$180(120- \frac{ 3 }{ 5 } x)x+60(12000-(120- \frac{ 3 }{ 5 } x)x)$$

Evaluate

$$72\left(x\left(200-x\right)+10000\right)$$

Solution Steps

Use the distributive property to multiply 180 by 120-\frac{3}{5}x.

$$\left(21600+180\left(-\frac{3}{5}\right)x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Express 180\left(-\frac{3}{5}\right) as a single fraction.

$$\left(21600+\frac{180\left(-3\right)}{5}x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Multiply 180 and -3 to get -540.

$$\left(21600+\frac{-540}{5}x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Divide -540 by 5 to get -108.

$$\left(21600-108x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Use the distributive property to multiply 21600-108x by x.

$$21600x-108x^{2}+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Use the distributive property to multiply 120-\frac{3}{5}x by x.

$$21600x-108x^{2}+60\left(12000-\left(120x-\frac{3}{5}xx\right)\right)$$

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

$$21600x-108x^{2}+60\left(12000-\left(120x-\frac{3}{5}x^{2}\right)\right)$$

To find the opposite of 120x-\frac{3}{5}x^{2}, find the opposite of each term.

$$21600x-108x^{2}+60\left(12000-120x-\left(-\frac{3}{5}x^{2}\right)\right)$$

The opposite of -\frac{3}{5}x^{2} is \frac{3}{5}x^{2}.

$$21600x-108x^{2}+60\left(12000-120x+\frac{3}{5}x^{2}\right)$$

Use the distributive property to multiply 60 by 12000-120x+\frac{3}{5}x^{2}.

$$21600x-108x^{2}[phone]x+60\times \frac{3}{5}x^{2}$$

Express 60\times \frac{3}{5} as a single fraction.

$$21600x-108x^{2}[phone]x+\frac{60\times 3}{5}x^{2}$$

Multiply 60 and 3 to get 180.

$$21600x-108x^{2}[phone]x+\frac{180}{5}x^{2}$$

Divide 180 by 5 to get 36.

$$21600x-108x^{2}[phone]x+36x^{2}$$

Combine 21600x and -7200x to get 14400x.

$$14400x-108x^{2}+720000+36x^{2}$$

Combine -108x^{2} and 36x^{2} to get -72x^{2}.

$$14400x-72x^{2}+720000$$

Expand

$$720000+14400x-72x^{2}$$

Solution Steps

Use the distributive property to multiply 180 by 120-\frac{3}{5}x.

$$\left(21600+180\left(-\frac{3}{5}\right)x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Express 180\left(-\frac{3}{5}\right) as a single fraction.

$$\left(21600+\frac{180\left(-3\right)}{5}x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Multiply 180 and -3 to get -540.

$$\left(21600+\frac{-540}{5}x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Divide -540 by 5 to get -108.

$$\left(21600-108x\right)x+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Use the distributive property to multiply 21600-108x by x.

$$21600x-108x^{2}+60\left(12000-\left(120-\frac{3}{5}x\right)x\right)$$

Use the distributive property to multiply 120-\frac{3}{5}x by x.

$$21600x-108x^{2}+60\left(12000-\left(120x-\frac{3}{5}xx\right)\right)$$

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

$$21600x-108x^{2}+60\left(12000-\left(120x-\frac{3}{5}x^{2}\right)\right)$$

To find the opposite of 120x-\frac{3}{5}x^{2}, find the opposite of each term.

$$21600x-108x^{2}+60\left(12000-120x-\left(-\frac{3}{5}x^{2}\right)\right)$$

The opposite of -\frac{3}{5}x^{2} is \frac{3}{5}x^{2}.

$$21600x-108x^{2}+60\left(12000-120x+\frac{3}{5}x^{2}\right)$$

Use the distributive property to multiply 60 by 12000-120x+\frac{3}{5}x^{2}.

$$21600x-108x^{2}[phone]x+60\times \frac{3}{5}x^{2}$$

Express 60\times \frac{3}{5} as a single fraction.

$$21600x-108x^{2}[phone]x+\frac{60\times 3}{5}x^{2}$$

Multiply 60 and 3 to get 180.

$$21600x-108x^{2}[phone]x+\frac{180}{5}x^{2}$$

Divide 180 by 5 to get 36.

$$21600x-108x^{2}[phone]x+36x^{2}$$

Combine 21600x and -7200x to get 14400x.

$$14400x-108x^{2}+720000+36x^{2}$$

Combine -108x^{2} and 36x^{2} to get -72x^{2}.

$$14400x-72x^{2}+720000$$