Solve for v 4v^2=28v

$4 v^{2} = 28 v$

Step 1

Subtract $28 v$ from both sides of the equation.

$4 v^{2} - 28 v = 0$

Step 2

Factor $4 v$ out of $4 v^{2} - 28 v$ .

Factor $4 v$ out of $4 v^{2}$ .

$4 v (v) - 28 v = 0$

Factor $4 v$ out of $- 28 v$ .

$4 v (v) + 4 v (- 7) = 0$

Factor $4 v$ out of $4 v (v) + 4 v (- 7)$ .

$4 v (v - 7) = 0$

Step 3

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

$v = 0$

$v - 7 = 0$

Step 4

Set $v$ equal to $0$ .

$v = 0$

Step 5

Set $v - 7$ equal to $0$ and solve for $v$ .

Set $v - 7$ equal to $0$ .

$v - 7 = 0$

Add $7$ to both sides of the equation.

$v = 7$

Step 6

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

$v = 0, 7$