Solve 5x=(7/5t-5)(4/5t-x)

$$5 x = ( \frac { 7 } { 5 } t - 5 ) ( \frac { 4 } { 5 } t - x )$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{4t}{5}-\frac{20}{7}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{5}t-5 by \frac{4}{5}t-x.

$$5x=\frac{28}{25}t^{2}-\frac{7}{5}tx-4t+5x$$

Add \frac{7}{5}tx to both sides.

$$5x+\frac{7}{5}tx=\frac{28}{25}t^{2}-4t+5x$$

Subtract 5x from both sides.

$$5x+\frac{7}{5}tx-5x=\frac{28}{25}t^{2}-4t$$

Combine 5x and -5x to get 0.

$$\frac{7}{5}tx=\frac{28}{25}t^{2}-4t$$

The equation is in standard form.

$$\frac{7t}{5}x=\frac{28t^{2}}{25}-4t$$

Divide both sides by \frac{7}{5}t.

$$\frac{5\times \frac{7t}{5}x}{7t}=\frac{5\left(\frac{28t^{2}}{25}-4t\right)}{7t}$$

Dividing by \frac{7}{5}t undoes the multiplication by \frac{7}{5}t.

$$x=\frac{5\left(\frac{28t^{2}}{25}-4t\right)}{7t}$$

Divide -4t+\frac{28t^{2}}{25} by \frac{7}{5}t.

$$x=\frac{4t}{5}-\frac{20}{7}$$

Solve for t

$$t=\frac{5x}{4}+\frac{25}{7}$$

$$t=0$$