Solve 4x(3-02x)+(100-4x)(1+x/20)/100

$$\frac{ 4x(3-02x)+(100-4x)(1+ \frac{ x }{ 20 } ) }{ 100 }$$

Evaluate

$$-\frac{x^{2}}{500}+\frac{13x}{100}+1$$

Short Solution Steps

Multiply 0 and 2 to get 0.

$$\frac{4x\left(3-0x\right)+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Anything times zero gives zero.

$$\frac{4x\left(3-0\right)+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Subtract 0 from 3 to get 3.

$$\frac{4x\times 3+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Multiply 4 and 3 to get 12.

$$\frac{12x+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{20}{20}.

$$\frac{12x+\left(100-4x\right)\left(\frac{20}{20}+\frac{x}{20}\right)}{100}$$

Since \frac{20}{20} and \frac{x}{20} have the same denominator, add them by adding their numerators.

$$\frac{12x+\left(100-4x\right)\times \frac{20+x}{20}}{100}$$

Express \left(100-4x\right)\times \frac{20+x}{20} as a single fraction.

$$\frac{12x+\frac{\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12x times \frac{20}{20}.

$$\frac{\frac{20\times 12x}{20}+\frac{\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

Since \frac{20\times 12x}{20} and \frac{\left(100-4x\right)\left(20+x\right)}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20\times 12x+\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

Do the multiplications in 20\times 12x+\left(100-4x\right)\left(20+x\right).

$$\frac{\frac{240x+2000+100x-80x-4x^{2}}{20}}{100}$$

Combine like terms in 240x+2000+100x-80x-4x^{2}.

$$\frac{\frac{260x+2000-4x^{2}}{20}}{100}$$

Express \frac{\frac{260x+2000-4x^{2}}{20}}{100} as a single fraction.

$$\frac{260x+2000-4x^{2}}{20\times 100}$$

Factor the expressions that are not already factored.

$$\frac{-4\left(x-\left(-\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)\left(x-\left(\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)}{20\times 100}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-\left(x-\left(-\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)\left(x-\left(\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)}{5\times 100}$$

Expand the expression.

$$\frac{-x^{2}+65x+500}{500}$$

Expand

$$-\frac{x^{2}}{500}+\frac{13x}{100}+1$$

Short Solution Steps

Multiply 0 and 2 to get 0.

$$\frac{4x\left(3-0x\right)+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Anything times zero gives zero.

$$\frac{4x\left(3-0\right)+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Subtract 0 from 3 to get 3.

$$\frac{4x\times 3+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

Multiply 4 and 3 to get 12.

$$\frac{12x+\left(100-4x\right)\left(1+\frac{x}{20}\right)}{100}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{20}{20}.

$$\frac{12x+\left(100-4x\right)\left(\frac{20}{20}+\frac{x}{20}\right)}{100}$$

Since \frac{20}{20} and \frac{x}{20} have the same denominator, add them by adding their numerators.

$$\frac{12x+\left(100-4x\right)\times \frac{20+x}{20}}{100}$$

Express \left(100-4x\right)\times \frac{20+x}{20} as a single fraction.

$$\frac{12x+\frac{\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12x times \frac{20}{20}.

$$\frac{\frac{20\times 12x}{20}+\frac{\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

Since \frac{20\times 12x}{20} and \frac{\left(100-4x\right)\left(20+x\right)}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20\times 12x+\left(100-4x\right)\left(20+x\right)}{20}}{100}$$

Do the multiplications in 20\times 12x+\left(100-4x\right)\left(20+x\right).

$$\frac{\frac{240x+2000+100x-80x-4x^{2}}{20}}{100}$$

Combine like terms in 240x+2000+100x-80x-4x^{2}.

$$\frac{\frac{260x+2000-4x^{2}}{20}}{100}$$

Express \frac{\frac{260x+2000-4x^{2}}{20}}{100} as a single fraction.

$$\frac{260x+2000-4x^{2}}{20\times 100}$$

Factor the expressions that are not already factored.

$$\frac{-4\left(x-\left(-\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)\left(x-\left(\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)}{20\times 100}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-\left(x-\left(-\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)\left(x-\left(\frac{5}{2}\sqrt{249}+\frac{65}{2}\right)\right)}{5\times 100}$$

Expand the expression.

$$\frac{-x^{2}+65x+500}{500}$$