The image you provided contains a mathematical expression that I can help simplify and solve. Here's what I can see clearly:

The problem is: $3(2x + 3)^2 - (x - 5) - (3x - 4)(x - 5)$

Step-by-step solution:

1. Expand the squared term $(2x + 3)^2$: $(2x + 3)^2 = (2x + 3)(2x + 3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9$ So: $3(2x + 3)^2 = 3(4x^2 + 12x + 9) = 12x^2 + 36x + 27$

2. Expand the product $(3x - 4)(x - 5)$ using the distributive property: $(3x - 4)(x - 5) = 3x(x - 5) - 4(x - 5) = 3x^2 - 15x - 4x + 20 = 3x^2 - 19x + 20$

3. Now we substitute these expansions into the original expression: $12x^2 + 36x + 27 - (x - 5) - (3x^2 - 19x + 20)$

4. Distribute the negative signs: $12x^2 + 36x + 27 - x + 5 - 3x^2 + 19x - 20$

5. Combine like terms: $(12x^2 - 3x^2) + (36x + 19x - x) + (27 + 5 - 20)$ Simplifying each group: $9x^2 + 54x + 12$

Final answer:

The simplified expression is: $9x^2 + 54x + 12$

Would you like any further clarification or more details on any steps? Here are some related questions to expand your understanding:

1. How do you approach expanding binomials like $(a + b)^2$?
2. Can you solve for the roots of a quadratic equation like $9x^2 + 54x + 12 = 0$?
3. How does distributing negative signs affect the terms in an equation?
4. How would you factor the final expression $9x^2 + 54x + 12$?
5. What are the applications of such algebraic expansions in real-life problems?

Tip: When expanding terms involving squares or products, always check for like terms that can simplify the expression!