Solve 5x*3(3-x/4)-7x/2

$$5 x \cdot 3 ( 3 - \frac { x } { 4 } ) - \frac { 7 x } { 2 }$$

Evaluate

$$\frac{x\left(166-15x\right)}{4}$$

Short Solution Steps

Multiply 5 and 3 to get 15.

$$15x\left(3-\frac{x}{4}\right)-\frac{7x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{4}{4}.

$$15x\left(\frac{3\times 4}{4}-\frac{x}{4}\right)-\frac{7x}{2}$$

Since \frac{3\times 4}{4} and \frac{x}{4} have the same denominator, subtract them by subtracting their numerators.

$$15x\times \frac{3\times 4-x}{4}-\frac{7x}{2}$$

Do the multiplications in 3\times 4-x.

$$15x\times \frac{12-x}{4}-\frac{7x}{2}$$

Express 15\times \frac{12-x}{4} as a single fraction.

$$\frac{15\left(12-x\right)}{4}x-\frac{7x}{2}$$

Use the distributive property to multiply 15 by 12-x.

$$\frac{180-15x}{4}x-\frac{7x}{2}$$

Express \frac{180-15x}{4}x as a single fraction.

$$\frac{\left(180-15x\right)x}{4}-\frac{7x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{7x}{2} times \frac{2}{2}.

$$\frac{\left(180-15x\right)x}{4}-\frac{2\times 7x}{4}$$

Since \frac{\left(180-15x\right)x}{4} and \frac{2\times 7x}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(180-15x\right)x-2\times 7x}{4}$$

Do the multiplications in \left(180-15x\right)x-2\times 7x.

$$\frac{180x-15x^{2}-14x}{4}$$

Combine like terms in 180x-15x^{2}-14x.

$$\frac{166x-15x^{2}}{4}$$

Expand

$$-\frac{15x^{2}}{4}+\frac{83x}{2}$$

Short Solution Steps

Multiply 5 and 3 to get 15.

$$15x\left(3-\frac{x}{4}\right)-\frac{7x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{4}{4}.

$$15x\left(\frac{3\times 4}{4}-\frac{x}{4}\right)-\frac{7x}{2}$$

Since \frac{3\times 4}{4} and \frac{x}{4} have the same denominator, subtract them by subtracting their numerators.

$$15x\times \frac{3\times 4-x}{4}-\frac{7x}{2}$$

Do the multiplications in 3\times 4-x.

$$15x\times \frac{12-x}{4}-\frac{7x}{2}$$

Express 15\times \frac{12-x}{4} as a single fraction.

$$\frac{15\left(12-x\right)}{4}x-\frac{7x}{2}$$

Use the distributive property to multiply 15 by 12-x.

$$\frac{180-15x}{4}x-\frac{7x}{2}$$

Express \frac{180-15x}{4}x as a single fraction.

$$\frac{\left(180-15x\right)x}{4}-\frac{7x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{7x}{2} times \frac{2}{2}.

$$\frac{\left(180-15x\right)x}{4}-\frac{2\times 7x}{4}$$

Since \frac{\left(180-15x\right)x}{4} and \frac{2\times 7x}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(180-15x\right)x-2\times 7x}{4}$$

Do the multiplications in \left(180-15x\right)x-2\times 7x.

$$\frac{180x-15x^{2}-14x}{4}$$

Combine like terms in 180x-15x^{2}-14x.

$$\frac{166x-15x^{2}}{4}$$