To solve the quadratic equation [tex]\((2x + 5)(3x - 4) = 0\)[/tex], we need to apply the zero product property, which states that if the product of two expressions is zero, at least one of the expressions must be zero. Therefore, we set each factor equal to zero and solve for [tex]\(x\)[/tex].
1. First factor:
[tex]\[
2x + 5 = 0
\][/tex]
To solve for [tex]\(x\)[/tex], we isolate [tex]\(x\)[/tex]:
[tex]\[
2x + 5 = 0 \implies 2x = -5 \implies x = -\frac{5}{2}
\][/tex]
2. Second factor:
[tex]\[
3x - 4 = 0
\][/tex]
Similarly, isolate [tex]\(x\)[/tex]:
[tex]\[
3x - 4 = 0 \implies 3x = 4 \implies x = \frac{4}{3}
\][/tex]
Thus, the solutions to the quadratic equation [tex]\((2x + 5)(3x - 4) = 0\)[/tex] are:
[tex]\[
x = -\frac{5}{2} \quad \text{and} \quad x = \frac{4}{3}
\][/tex]
So the correct answer is:
C. [tex]\(-\frac{5}{2}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex]
