I gotchu!

Step-by-step explanation:

1. Factor: The given equation is g(x) = x(x+4)(x-3).

2. x-intercepts: To find the x-intercepts, set g(x) = 0.

x(x+4)(x-3) = 0

x = 0, -4, 3

x-intercepts: (0,0), (-4,0), (3,0)

3. y-intercept: Plug in x = 0 to find the y-intercept.

g(0) = 0(0+4)(0-3) = 0

y-intercept: (0,0)

4. Complete solution: To solve g(x) = 12x, we need to find the x-values for which g(x) is equal to 12x.

x(x+4)(x-3) = 12x

x^3 + x^2 - 3x = 12x

x^3 + x^2 - 15x = 0

x(x^2 + x - 15) = 0

x(x+5)(x-3) = 0

x = 0, -5, 3

Solution: x-values for which g(x) = 12x are x = 0, -5, 3.

5. Graph: To graph the function g(x) = x(x+4)(x-3), plot the x-intercepts and the y-intercept. Then, sketch a smooth curve passing through these points.

The graph should include the points (0,0), (-4,0), (3,0), and (0,0).

The shape of the graph will depend on the signs of the factors (x, x+4, and x-3).

You can also use a graphing calculator or online graphing tool to visualize the graph!

NOTE: I hope this helps!