(x+1)(x^2+2x+4)-x^3-3x^2+16=0

2 min read Jun 16, 2024

Solving the Equation: (x+1)(x^2+2x+4)-x^3-3x^2+16=0

This article will guide you through the process of solving the equation (x+1)(x^2+2x+4)-x^3-3x^2+16=0. We will break down each step and explain the reasoning behind it.

1. Expanding the Equation

First, we need to expand the left side of the equation. We can do this by multiplying out the brackets:

(x+1)(x^2+2x+4) = x(x^2+2x+4) + 1(x^2+2x+4) = x^3 + 2x^2 + 4x + x^2 + 2x + 4 = x^3 + 3x^2 + 6x + 4

Now our equation looks like this: x^3 + 3x^2 + 6x + 4 - x^3 - 3x^2 + 16 = 0

2. Simplifying the Equation

Next, we can simplify the equation by combining like terms:

6x + 20 = 0

3. Isolating the Variable

To isolate the variable x, we need to subtract 20 from both sides of the equation:

6x = -20

4. Solving for x

Finally, we can solve for x by dividing both sides of the equation by 6:

x = -20/6

5. Simplifying the Solution

The solution can be further simplified:

x = -10/3

Therefore, the solution to the equation (x+1)(x^2+2x+4)-x^3-3x^2+16=0 is x = -10/3.