Solve for j (2j+9)(3j-2)=0

$(2 j + 9) (3 j - 2) = 0$

Step 1

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

$2 j + 9 = 0$

$3 j - 2 = 0$

Step 2

Set $2 j + 9$ equal to $0$ and solve for $j$ .

Set $2 j + 9$ equal to $0$ .

$2 j + 9 = 0$

Solve $2 j + 9 = 0$ for $j$ .

Subtract $9$ from both sides of the equation.

$2 j = - 9$

Divide each term in $2 j = - 9$ by $2$ and simplify.

Divide each term in $2 j = - 9$ by $2$ .

$\frac{2 j}{2} = \frac{- 9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 j}{2} = \frac{- 9}{2}$

Divide $j$ by $1$ .

$j = \frac{- 9}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$j = - \frac{9}{2}$

Step 3

Set $3 j - 2$ equal to $0$ and solve for $j$ .

Set $3 j - 2$ equal to $0$ .

$3 j - 2 = 0$

Solve $3 j - 2 = 0$ for $j$ .

Add $2$ to both sides of the equation.

$3 j = 2$

Divide each term in $3 j = 2$ by $3$ and simplify.

Divide each term in $3 j = 2$ by $3$ .

$\frac{3 j}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 j}{3} = \frac{2}{3}$

Divide $j$ by $1$ .

$j = \frac{2}{3}$

Step 4

The final solution is all the values that make $(2 j + 9) (3 j - 2) = 0$ true.

$j = - \frac{9}{2}, \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$j = - \frac{9}{2}, \frac{2}{3}$

Decimal Form:

$j = - 4.5, 0.\overline{6}$

Mixed Number Form:

$j = - 4 \frac{1}{2}, \frac{2}{3}$

Solve for j (2j+9)(3j-2)=0

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