We can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. So we set each factor equal to zero and solve for `x`:
```
(x - 2)² = 0 or 2x + 3 = 0
```
For the first factor, we can take the square root of both sides:
```
x - 2 = 0
```
Adding 2 to both sides, we get:
```
x = 2
```
For the second factor, we can subtract 3 from both sides:
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soit (x-2)² = 0 donc x = 2
soit (2x+3) = 0 donc x = -3/2
2 solutions
Verified answer
Réponse:
To solve the equation:
```
(x - 2)² (2x + 3) = 0
```
We can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. So we set each factor equal to zero and solve for `x`:
```
(x - 2)² = 0 or 2x + 3 = 0
```
For the first factor, we can take the square root of both sides:
```
x - 2 = 0
```
Adding 2 to both sides, we get:
```
x = 2
```
For the second factor, we can subtract 3 from both sides:
```
2x = -3
```
Dividing both sides by 2, we get:
```
x = -3/2
```
Therefore, the solutions to the equation are:
```
x = 2 or x = -3/2
```