Solve for u 6u^2+18u=0

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

Step 1

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 2

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 3

Set $u$ equal to $0$ .

$u = 0$

Step 4

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

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

$u + 3 = 0$

Subtract $3$ from both sides of the equation.

$u = - 3$

Step 5

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

$u = 0, - 3$