Sure! Let's solve the equation [tex]\((x + 1)(x - 3) = 0\)[/tex] step by step.
1. Identify the roots of the equation:
To solve [tex]\((x + 1)(x - 3) = 0\)[/tex], we need to find the values of [tex]\(x\)[/tex] that make the equation true. In other words, we need to figure out when the product [tex]\((x + 1)\)[/tex] and [tex]\((x - 3)\)[/tex] equals zero.
2. Set each factor to zero:
For the product of two expressions to be zero, at least one of the expressions must be zero. So, we set each factor equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[
x + 1 = 0
\][/tex]
[tex]\[
x - 3 = 0
\][/tex]
3. Solve each equation:
- For the first equation [tex]\(x + 1 = 0\)[/tex]:
[tex]\[
x = -1
\][/tex]
- For the second equation [tex]\(x - 3 = 0\)[/tex]:
[tex]\[
x = 3
\][/tex]
4. Combine the solutions:
The solutions to the equation [tex]\((x + 1)(x - 3) = 0\)[/tex] are the values of [tex]\(x\)[/tex] we found from each factor:
[tex]\[
x = -1 \quad \text{and} \quad x = 3
\][/tex]
Therefore, the solutions to the equation [tex]\((x + 1)(x - 3) = 0\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = 3\)[/tex].
