To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:
1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:
4x3 + 5x = -21
2. Factor out x from the left-hand side of the equation:
x(4x2 + 5) = -21
3. Divide both sides by (4x2 + 5):
x = -21 / (4x2 + 5)
So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.