To solve the quadratic equation [tex]\((x-3)(x+2) = 0\)[/tex], we can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Given the equation:
[tex]\[
(x - 3)(x + 2) = 0
\][/tex]
We can set each factor equal to zero and solve for [tex]\(x\)[/tex]:
1. For the first factor:
[tex]\[
x - 3 = 0
\][/tex]
Add 3 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 3
\][/tex]
2. For the second factor:
[tex]\[
x + 2 = 0
\][/tex]
Subtract 2 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x = -2
\][/tex]
So, the solutions to the equation [tex]\((x-3)(x+2) = 0\)[/tex] are [tex]\(x = 3\)[/tex] and [tex]\(x = -2\)[/tex].
The solution with the lowest value is:
[tex]\[
x = -2
\][/tex]
