Solve for b 9b^2+0.27b=0

$9 b^{2} + 0.27 b = 0$

Step 1

Factor $0.09 b$ out of $9 b^{2} + 0.27 b$ .

Factor $0.09 b$ out of $9 b^{2}$ .

$0.09 b (100 b) + 0.27 b = 0$

Factor $0.09 b$ out of $0.27 b$ .

$0.09 b (100 b) + 0.09 b (3) = 0$

Factor $0.09 b$ out of $0.09 b (100 b) + 0.09 b (3)$ .

$0.09 b (100 b + 3) = 0$

Step 2

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

$b = 0$

$100 b + 3 = 0$

Step 3

Set $b$ equal to $0$ .

$b = 0$

Step 4

Set $100 b + 3$ equal to $0$ and solve for $b$ .

Set $100 b + 3$ equal to $0$ .

$100 b + 3 = 0$

Solve $100 b + 3 = 0$ for $b$ .

Subtract $3$ from both sides of the equation.

$100 b = - 3$

Divide each term in $100 b = - 3$ by $100$ and simplify.

Divide each term in $100 b = - 3$ by $100$ .

$\frac{100 b}{100} = \frac{- 3}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 b}{100} = \frac{- 3}{100}$

Divide $b$ by $1$ .

$b = \frac{- 3}{100}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{3}{100}$

Step 5

The final solution is all the values that make $0.09 b (100 b + 3) = 0$ true.

$b = 0, - \frac{3}{100}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = 0, - \frac{3}{100}$

Decimal Form:

$b = 0, - 0.03$