Solve by Factoring 16x^2=56x

$16 x^{2} = 56 x$

Step 1

Subtract $56 x$ from both sides of the equation.

$16 x^{2} - 56 x = 0$

Step 2

Factor $8 x$ out of $16 x^{2} - 56 x$ .

Factor $8 x$ out of $16 x^{2}$ .

$8 x (2 x) - 56 x = 0$

Factor $8 x$ out of $- 56 x$ .

$8 x (2 x) + 8 x (- 7) = 0$

Factor $8 x$ out of $8 x (2 x) + 8 x (- 7)$ .

$8 x (2 x - 7) = 0$

Step 3

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

$x = 0$

$2 x - 7 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $2 x - 7$ equal to $0$ and solve for $x$ .

Set $2 x - 7$ equal to $0$ .

$2 x - 7 = 0$

Solve $2 x - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$2 x = 7$

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

Step 6

The final solution is all the values that make $8 x (2 x - 7) = 0$ true.

$x = 0, \frac{7}{2}$