Solve 2/5*(x-5)=5*(x-2/5)

$$\frac { 2 } { 5 } \cdot ( x - 5 ) = 5 \cdot ( x - \frac { 2 } { 5 } )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{5}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

$$\frac{2}{5}x+\frac{-10}{5}=5\left(x-\frac{2}{5}\right)$$

Divide -10 by 5 to get -2.

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

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

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

Cancel out 5 and 5.

$$\frac{2}{5}x-2=5x-2$$

Subtract 5x from both sides.

$$\frac{2}{5}x-2-5x=-2$$

Combine \frac{2}{5}x and -5x to get -\frac{23}{5}x.

$$-\frac{23}{5}x-2=-2$$

Add 2 to both sides.

$$-\frac{23}{5}x=-2+2$$

Add -2 and 2 to get 0.

$$-\frac{23}{5}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{23}{5} is not equal to 0, x must be equal to 0.

$$x=0$$