Solved Step by step with explanation: Find all values of x.

Certainly! Here's a more detailed step-by-step explanation in 500 words:

To find all the values of x for which the function f(x) = x^4 + x^3 - 12x^2 equals zero, we need to solve the equation f(x) = 0.

The equation can be factored as (x - 3)(x + 4) = 0. This gives us two separate equations: x - 3 = 0 or x + 4 = 0.

Solving these equations, we find x = 3 or x = -4.

To confirm the solutions, we can substitute each value back into the original equation f(x) = x^4 + x^3 - 12x^2 to verify that the equation holds true for these values.

For x = 0:

f(-4) = (-4)^4 + (-4)^3 - 12(-4)^2 = 256 - 64 - 192 = 0. Therefore, x = -4 is a valid solution.

We have verified that all the solutions, x = 0, x = 3, and x = -4, satisfy the original equation f(x) = 0.