Let's start by simplifying and solving the equation:

\[
6x^2 - 11x - 7 = 6x^2 + 10x - 16
\]

### Step 1: Subtract \(6x^2\) from both sides

Since \(6x^2\) appears on both sides of the equation, we can subtract \(6x^2\) from both sides:

\[
-11x - 7 = 10x - 16
\]

### Step 2: Combine like terms

To simplify, we'll move all the \(x\) terms to one side and the constant terms to the other side. First, add \(11x\) to both sides:

\[
-7 = 21x - 16
\]

Next, add \(16\) to both sides:

\[
9 = 21x
\]

### Step 3: Solve for \(x\)

Finally, divide both sides by 21 to solve for \(x\):

\[
x = \frac{9}{21} = \frac{3}{7}
\]

### Final Answer:
\[
x = \frac{3}{7}
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions for further practice:

1. What would happen if the coefficients in the equation were different?
2. Can you solve an equation where one side is a quadratic trinomial and the other is a linear expression?
3. How would you approach solving this equation if the quadratic terms did not cancel out?
4. What is the graphical interpretation of solving this equation?
5. How can you verify the solution using substitution?

**Tip:** When both sides of an equation have the same quadratic term, it often simplifies to a linear equation, making it easier to solve.

Learn how to solve the quadratic equation 6x^2 - 11x - 7 = 6x^2 + 10x - 16 step-by-step with detailed explanations and practice questions. This problem involves algebraic manipulation and solving quadratic equations. Suitable for high school students in Grades 9-12.

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