Final answer:
The question asks to solve a quadratic equation, 32b(3/4-5b) = 10, which simplifies to 160b^2 - 24b + 10 = 0. This can be solved for the variable b using the quadratic formula.
Step-by-step explanation:
To solve the equation 32b(3/4-5b) = 10, we need to simplify and solve for b. First, distribute 32b to the terms inside the parentheses:
32b * (3/4) - 32b * (5b) = 10
24b - 160b^2 = 10
Now we have a quadratic equation in the form of ab^2 + bb + c = 0 once we move all terms to one side and change signs:
160b^2 - 24b + 10 = 0
This is a standard form quadratic equation, and we can solve for b using the quadratic formula or by factoring if the equation is factorable. Since this equation does not factor neatly, we would typically use the quadratic formula:
b = (-b ± √(b^2 - 4ac)) / (2a)