It sounds like you're working on an equation that has two solutions: 6 and -1. These could be the solutions to a quadratic equation, or they may come from a system of equations.

One common form that produces two solutions is a quadratic equation like this:

\[
x^2 + bx + c = 0
\]

If we assume the solutions are \(x = 6\) and \(x = -1\), we can construct the factors of the quadratic equation using the reverse process:

\[
(x - 6)(x + 1) = 0
\]

Expanding this gives:

\[
x^2 + x - 6x - 6 = 0
\]
\[
x^2 - 5x - 6 = 0
\]

So, the quadratic equation is:

\[
x^2 - 5x - 6 = 0
\]

If your solutions come from a different equation, feel free to share more details so I can provide a more tailored explanation.

Would you like me to dive deeper into how this works or clarify something specific?

Here are 5 related questions:
1. How do you factor a quadratic equation to find solutions?
2. What does the quadratic formula look like, and when is it useful?
3. How can we verify if 6 and -1 are correct solutions for this quadratic equation?
4. Can all quadratic equations be factored neatly like this one?
5. How do the coefficients of a quadratic equation affect its graph?

**Tip**: When solving quadratic equations, always check if it can be factored easily before applying more complex methods like the quadratic formula.

Learn how to solve the quadratic equation x^2 - 5x - 6, which gives the solutions 6 and -1. This detailed explanation covers factoring and key algebraic principles. Suitable for Grades 7-9 students.

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