Solve by Factoring 3x^2=5x

$3 x^{2} = 5 x$

Step 1

Subtract $5 x$ from both sides of the equation.

$3 x^{2} - 5 x = 0$

Step 2

Factor $x$ out of $3 x^{2} - 5 x$ .

Factor $x$ out of $3 x^{2}$ .

$x (3 x) - 5 x = 0$

Factor $x$ out of $- 5 x$ .

$x (3 x) + x \cdot - 5 = 0$

Factor $x$ out of $x (3 x) + x \cdot - 5$ .

$x (3 x - 5) = 0$

Step 3

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

$x = 0$

$3 x - 5 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $3 x - 5$ equal to $0$ and solve for $x$ .

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Solve $3 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$3 x = 5$

Divide each term in $3 x = 5$ by $3$ and simplify.

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 6

The final solution is all the values that make $x (3 x - 5) = 0$ true.

$x = 0, \frac{5}{3}$