Solving the Algebraic Equation

The problem requires finding the value of the variable x in the given algebraic equation.

$2(3x^2 - 7) - 3(2x^2 + 7x - 9) = 13$

Step-by-Step Solution to Find x

1. Expand Terms: Distribute the constants outside the parentheses to the terms inside.

   $ (2 \times 3x^2 - 2 \times 7) - (3 \times 2x^2 + 3 \times 7x - 3 \times 9) = 13 $

   $ (6x^2 - 14) - (6x^2 + 21x - 27) = 13 $

2. Simplify the Equation: Remove the parentheses, paying attention to the negative sign before the second set. Combine like terms.

   $ 6x^2 - 14 - 6x^2 - 21x + 27 = 13 $

   Combine the $x^2$ terms: $6x^2 - 6x^2 = 0$.
   Combine the constant terms: $-14 + 27 = 13$.
   The simplified equation is:

   $ -21x + 13 = 13 $

3. Isolate the Variable Term: Subtract 13 from both sides of the equation to isolate the term containing x.

   $ -21x = 13 - 13 $

   $ -21x = 0 $

4. Solve for x: Divide both sides by the coefficient of x, which is -21.

   $ x = \frac{0}{-21} $

   $ x = 0 $

The value of x that satisfies the equation is 0.