Solving the Equation for x

We need to find the value of x that satisfies the given equation:

$5(5x^2 - 6) - 5(5x^2 + 2x - 4) = 20$

Step-by-Step Simplification

1. Distribute the number 5 into the first parenthesis:

   $ (5 \times 5x^2) - (5 \times 6) = 25x^2 - 30 $

2. Distribute the number 5 into the second parenthesis:

   $ 5(5x^2 + 2x - 4) = (5 \times 5x^2) + (5 \times 2x) - (5 \times 4) = 25x^2 + 10x - 20 $

3. Substitute these expanded forms back into the original equation:

   $ (25x^2 - 30) - (25x^2 + 10x - 20) = 20 $

4. Distribute the negative sign (-) to the terms inside the second parenthesis:

   $ 25x^2 - 30 - 25x^2 - 10x + 20 = 20 $

5. Combine like terms. Notice that the $25x^2$ terms cancel each other out ($25x^2 - 25x^2 = 0$):

   $ (25x^2 - 25x^2) - 10x + (-30 + 20) = 20 $

   $ 0 - 10x - 10 = 20 $

   $ -10x - 10 = 20 $

6. Isolate the term with x by adding 10 to both sides of the equation:

   $ -10x - 10 + 10 = 20 + 10 $

   $ -10x = 30 $

7. Solve for x by dividing both sides by -10:

   $ x = \frac{30}{-10} $

   $ x = -3 $

Therefore, the value of x satisfying the equation is -3.