(x%5E2%2B3x%2B9)%2Bx(5-x%5E2)%3D6x.jpeg "(x-3)(x^2+3x+9)+x(5-x^2)=6x")
Solving the Equation: (x-3)(x^2+3x+9)+x(5-x^2)=6x
In this article, we will solve the equation (x-3)(x^2+3x+9)+x(5-x^2)=6x and find the values of x that satisfy the equation.
Step 1: Expand the Left-Hand Side
Let's start by expanding the left-hand side of the equation using the distributive property:
(x-3)(x^2+3x+9) = x^3 + 3x^2 + 9x - 3x^2 - 9x - 27
= x^3 - 6x - 27
Step 2: Expand the Second Term
Next, let's expand the second term:
x(5-x^2) = 5x - x^3
Step 3: Combine the Terms
Now, let's combine the two expanded terms:
x^3 - 6x - 27 + 5x - x^3 = 6x
Simplify the equation by combining like terms:
-x - 27 + 5x = 6x
Step 4: Solve for x
Rearrange the equation to get all the terms on one side:
-x + 5x - 6x = 27
Combine like terms:
-2x = 27
Divide both sides by -2 to solve for x:
x = -27/2
x = -13.5
Therefore, the solution to the equation is x = -13.5.
