Solve A=2x/5(3x-6/9)

$$A = \frac { 2 x } { 5 } ( 3 x - \frac { 6 } { 9 } )$$

Solve for A

$$A=\frac{2x\left(9x-2\right)}{15}$$

Short Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

Use the distributive property to multiply \frac{2x}{5} by 3x-\frac{2}{3}.

$$A=3\times \frac{2x}{5}x-\frac{2}{3}\times \frac{2x}{5}$$

Express 3\times \frac{2x}{5} as a single fraction.

$$A=\frac{3\times 2x}{5}x-\frac{2}{3}\times \frac{2x}{5}$$

Express \frac{3\times 2x}{5}x as a single fraction.

$$A=\frac{3\times 2xx}{5}-\frac{2}{3}\times \frac{2x}{5}$$

Multiply -\frac{2}{3} times \frac{2x}{5} by multiplying numerator times numerator and denominator times denominator.

$$A=\frac{3\times 2xx}{5}+\frac{-2\times 2x}{3\times 5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3\times 5 is 3\times 5. Multiply \frac{3\times 2xx}{5} times \frac{3}{3}.

$$A=\frac{3\times 3\times 2xx}{3\times 5}+\frac{-2\times 2x}{3\times 5}$$

Since \frac{3\times 3\times 2xx}{3\times 5} and \frac{-2\times 2x}{3\times 5} have the same denominator, add them by adding their numerators.

$$A=\frac{3\times 3\times 2xx-2\times 2x}{3\times 5}$$

Do the multiplications in 3\times 3\times 2xx-2\times 2x.

$$A=\frac{18x^{2}-4x}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$A=\frac{18x^{2}-4x}{15}$$

Divide each term of 18x^{2}-4x by 15 to get \frac{6}{5}x^{2}-\frac{4}{15}x.

$$A=\frac{6}{5}x^{2}-\frac{4}{15}x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{270A+4}}{18}+\frac{1}{9}$$

$$x=-\frac{\sqrt{270A+4}}{18}+\frac{1}{9}$$

Solve for x

$$x=\frac{\sqrt{270A+4}}{18}+\frac{1}{9}$$

$$x=-\frac{\sqrt{270A+4}}{18}+\frac{1}{9}\text{, }A\geq -\frac{2}{135}$$