We need to solve the equation for `x`

Remove the fraction by multiplying the first term of the factor by the denominator of the secondterm. `(x+3)(2x+3)=0 ` Set each of the factors of the left-hand side of the equation equal to `0` . `x+3=0` `2x+3=0 ` Since `3`...

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We need to solve the equation for `x`

Remove the fraction by multiplying the first term of the factor by the denominator of the second term.

`(x+3)(2x+3)=0 `

Set each of the factors of the left-hand side of the equation equal to `0` .

`x+3=0`

`2x+3=0 `

Since `3` does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting `3` from both sides.

`x=-3 `

`2x+3=0 `

Set each of the factors of the left-hand side of the equation equal to `0` .

`x=-3 `

`2x+3=0`

Since `3` does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting `3` from both sides.

`x=-3 `

`2x=-3 `

Divide each term in the equation by `2` .

`x=-3 `

`x = -3/2`

The complete solution is the set of the individual solutions.

`x = -3, -3/2`

Solve `2x^2 + 9x + 9 = 0` .

Factor: `(2x + 3)(x+3) = 0` .

Using the zero product property, set each factor equal to zero and solve.

`2x+3 = 0` and `x + 3 = 0`

`2x = -3` and `x = -3`

`x = -3/2` and` x=-3`

**The solutions are `x = - 3` and `x = -3/2.`**

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