Final answer:
The values of x for which the equation y = 4x^3 - 9x^2 - 12x + 7 holds true are x = -1, x = 1/2, and x = 7/2.
Step-by-step explanation:
To find the values of x for which the given equation y = 4x^3 - 9x^2 - 12x + 7 holds true, we need to set y equal to zero and solve for x.
Let's set y = 0:
0 = 4x^3 - 9x^2 - 12x + 7
Now, we can factor the equation or use a numerical method like the Rational Root Theorem to find the roots.
Using a numerical method, we can see that x = -1, 1/2, and 7/2 are the roots of the equation.
Therefore, the values of x for which the equation holds true are x = -1, x = 1/2, and x = 7/2.