To solve the equation \( 25x^2 - 36 = (5x + 9)(5x - 4) \), let's begin by expanding the right-hand side:

1. Expand the expression on the right-hand side using the distributive property (FOIL):
\[
(5x + 9)(5x - 4) = 5x(5x) + 5x(-4) + 9(5x) + 9(-4)
\]
\[
= 25x^2 - 20x + 45x - 36
\]
\[
= 25x^2 + 25x - 36
\]

Now, the equation becomes:
\[
25x^2 - 36 = 25x^2 + 25x - 36
\]

2. Subtract \( 25x^2 - 36 \) from both sides to simplify:
\[
0 = 25x
\]

3. Divide both sides by 25:
\[
x = 0
\]

Thus, the solution to the equation is \( x = 0 \).

Would you like more details or have any questions? Here are 5 related questions:

1. What is the significance of factoring in solving quadratic equations?
2. How do you use the distributive property to expand binomials?
3. Can quadratic equations have more than one solution?
4. What happens when both sides of the equation contain the same quadratic term?
5. How can you verify the solution of an equation?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it holds.

Learn how to solve the quadratic equation 25x² - 36 = (5x + 9)(5x - 4) with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring, the distributive property, and the zero product property. Suitable for students in Grades 9-11.

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