To solve the equation [tex]\(7h(2h - 3) = 0\)[/tex], we need to find the values of [tex]\(h\)[/tex] that satisfy this equation. Let's go through the steps:
1. Understand the equation: The equation [tex]\(7h(2h - 3) = 0\)[/tex] is a product of two terms. For a product to be zero, at least one of the terms must be zero.
2. Set each factor to zero: We can set up two separate equations by setting each factor in the product [tex]\(7h(2h - 3) = 0\)[/tex] to zero.
- The first factor is [tex]\(7h\)[/tex].
- The second factor is [tex]\((2h - 3)\)[/tex].
3. Solve for [tex]\(h\)[/tex] in each case:
- Case 1: Set the first factor, [tex]\(7h\)[/tex], equal to zero:
[tex]\[
7h = 0
\][/tex]
To solve this equation, divide both sides by 7:
[tex]\[
h = 0
\][/tex]
So, one solution is [tex]\(h = 0\)[/tex].
- Case 2: Set the second factor, [tex]\((2h - 3)\)[/tex], equal to zero:
[tex]\[
2h - 3 = 0
\][/tex]
To solve for [tex]\(h\)[/tex], add 3 to both sides:
[tex]\[
2h = 3
\][/tex]
Then divide both sides by 2:
[tex]\[
h = \frac{3}{2}
\][/tex]
So, another solution is [tex]\(h = 1.5\)[/tex].
4. Combine the solutions: The equation [tex]\(7h(2h - 3) = 0\)[/tex] has two solutions:
[tex]\[
h = 0 \quad \text{and} \quad h = 1.5
\][/tex]
Therefore, the solutions to the equation [tex]\(7h(2h - 3) = 0\)[/tex] are [tex]\(h = 0\)[/tex] and [tex]\(h = 1.5\)[/tex].
