(x-3)(x^2+3x+9)+x(5-x^2)=6x

2 min read Jun 17, 2024

Solving the Equation (x-3)(x^2+3x+9)+x(5-x^2)=6x

This article will guide you through solving the equation (x-3)(x^2+3x+9)+x(5-x^2)=6x. We'll break down the steps and explain each operation to help you understand the process.

Step 1: Expand the Products

First, we need to expand the products using the distributive property:

(x-3)(x^2+3x+9):
- x(x^2+3x+9) - 3(x^2+3x+9)
- x^3 + 3x^2 + 9x - 3x^2 - 9x - 27
- x^3 - 27
x(5-x^2):
- 5x - x^3

Now, let's rewrite the equation with the expanded products:

x^3 - 27 + 5x - x^3 = 6x

Step 2: Simplify the Equation

Notice that the x^3 terms cancel out:

-27 + 5x = 6x

Step 3: Isolate the x Term

Subtract 5x from both sides:

-27 = x

Solution

Therefore, the solution to the equation (x-3)(x^2+3x+9)+x(5-x^2)=6x is x = -27.