Final answer:
To find the value of t that makes the equation true, distribute and simplify the equation, then rearrange it to get 0 on one side. Finally, solve for t using the quadratic formula.
Step-by-step explanation:
To find the value of t that makes the equation true, we need to simplify the equation and then solve for t. First, we distribute the terms on the left side of the equation:
(4x + 5)(2x^2 + 3) = 86 + t + 15
Expanding the expression gives us:
8x^3 + 12x^2 + 10x + 15 = 101 + t
Next, rearrange the equation to get 0 on one side:
8x^3 + 12x^2 + 10x - 86 - t = 0
Now, the equation is in the form of a quadratic equation. We can solve for t using the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values a = 8, b = 10, and c = -86, we can calculate the value of t that makes the equation true.