Solve by Factoring 7x^2=4x

$7 x^{2} = 4 x$

Step 1

Subtract $4 x$ from both sides of the equation.

$7 x^{2} - 4 x = 0$

Step 2

Factor $x$ out of $7 x^{2} - 4 x$ .

Factor $x$ out of $7 x^{2}$ .

$x (7 x) - 4 x = 0$

Factor $x$ out of $- 4 x$ .

$x (7 x) + x \cdot - 4 = 0$

Factor $x$ out of $x (7 x) + x \cdot - 4$ .

$x (7 x - 4) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$7 x - 4 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $7 x - 4$ equal to $0$ and solve for $x$ .

Set $7 x - 4$ equal to $0$ .

$7 x - 4 = 0$

Solve $7 x - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$7 x = 4$

Divide each term in $7 x = 4$ by $7$ and simplify.

Divide each term in $7 x = 4$ by $7$ .

$\frac{7 x}{7} = \frac{4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{4}{7}$

Divide $x$ by $1$ .

$x = \frac{4}{7}$

Step 6

The final solution is all the values that make $x (7 x - 4) = 0$ true.

$x = 0, \frac{4}{7}$