Solve for u 6u^2=18u

$6 u^{2} = 18 u$

Step 1

Subtract $18 u$ from both sides of the equation.

$6 u^{2} - 18 u = 0$

Step 2

Factor $6 u$ out of $6 u^{2} - 18 u$ .

Factor $6 u$ out of $6 u^{2}$ .

$6 u (u) - 18 u = 0$

Factor $6 u$ out of $- 18 u$ .

$6 u (u) + 6 u (- 3) = 0$

Factor $6 u$ out of $6 u (u) + 6 u (- 3)$ .

$6 u (u - 3) = 0$

Step 3

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

$u = 0$

$u - 3 = 0$

Step 4

Set $u$ equal to $0$ .

$u = 0$

Step 5

Set $u - 3$ equal to $0$ and solve for $u$ .

Set $u - 3$ equal to $0$ .

$u - 3 = 0$

Add $3$ to both sides of the equation.

$u = 3$

Step 6

The final solution is all the values that make $6 u (u - 3) = 0$ true.

$u = 0, 3$