To solve the equation \(-3(4a + 3) + 4(6a + 1) = 43\), we can follow these steps:

1. **Distribute** the \(-3\) and \(4\) to the terms inside the parentheses:
   \[
   -3(4a) - 3(3) + 4(6a) + 4(1) = 43
   \]
   Simplify each term:
   \[
   -12a - 9 + 24a + 4 = 43
   \]

2. **Combine like terms**:
   \[
   (-12a + 24a) + (-9 + 4) = 43
   \]
   Simplify:
   \[
   12a - 5 = 43
   \]

3. **Add 5** to both sides to isolate the term with \(a\):
   \[
   12a = 43 + 5
   \]
   \[
   12a = 48
   \]

4. **Divide** both sides by 12 to solve for \(a\):
   \[
   a = \frac{48}{12}
   \]
   \[
   a = 4
   \]

So, the solution is \(a = 4\).

Would you like any further explanation or have any other questions?

Here are 5 related questions:
1. How would you solve \(2(5b - 3) - 4(b + 2) = 8\)?
2. What happens if the equation was \(-3(4a + 3) + 4(6a + 1) = 0\) instead?
3. Can you solve \(5(2a + 1) - 3(4a - 2) = 17\)?
4. How would the solution change if the equation was \(-3(4a + 3) + 4(6a + 1) = 100\)?
5. What if the equation had fractions, like \(-\frac{1}{2}(4a + 3) + \frac{2}{3}(6a + 1) = \frac{7}{6}\)?

**Tip:** When solving equations, always combine like terms and simplify as much as possible before isolating the variable.

Learn how to solve the equation -3(4a + 3) + 4(6a + 1) = 43 with a detailed step-by-step solution. This problem involves linear equations, the distributive property, and combining like terms. Suitable for Grades 7-9 students learning algebraic equations.

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