Solve by Factoring 3x^2+5x=8x

$3 x^{2} + 5 x = 8 x$

Step 1

Subtract $8 x$ from both sides of the equation.

$3 x^{2} + 5 x - 8 x = 0$

Step 2

Subtract $8 x$ from $5 x$ .

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

Step 3

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

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

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

Factor $3 x$ out of $- 3 x$ .

$3 x (x) + 3 x (- 1) = 0$

Factor $3 x$ out of $3 x (x) + 3 x (- 1)$ .

$3 x (x - 1) = 0$

Step 4

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

$x = 0$

$x - 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $3 x (x - 1) = 0$ true.

$x = 0, 1$