Answer:
x = -1
Explanation:
To solve this equation, you can use the process of polynomial algebra.
First, you can rearrange the terms on the left side of the equation so that all the terms with an x^2 coefficient are on one side and all the other terms are on the other side. You can do this by adding x^2 to both sides of the equation:
5x^2 - 2x - 6 + x^2 = -x^2 + 6x + x^2
This gives you:
6x^2 - 2x - 6 = 6x
Now, you can rearrange the terms on the right side of the equation in the same way:
6x^2 - 2x - 6 = 6x^2 - 6x
To solve for x, you can now use the process of polynomial algebra to combine like terms on each side of the equation. This gives you:
6x^2 - 2x - 6 = 6x^2 - 6x
Combining like terms on the left side of the equation gives you:
6x^2 - 6x - 6 = 6x^2 - 6x
Combining like terms on the right side of the equation gives you:
6x^2 - 6x - 6 = 6x^2 - 6x
Now, you can subtract 6x^2 - 6x from both sides of the equation to obtain:
-6x - 6 = 0
Dividing both sides of the equation by -6 gives you:
x + 1 = 0
Finally, you can solve for x by subtracting 1 from both sides of the equation, which gives you:
x = -1
Therefore, the solution to the original equation is x = -1.