Let's solve the equation step by step.

The given equation is:

\[
5 \times 2 \times x(x - 3) - 6x(x + 7)
\]

First, simplify the multiplication:

\[
5 \times 2 = 10
\]

So, the equation becomes:

\[
10x(x - 3) - 6x(x + 7)
\]

Next, distribute the terms:

\[
10x(x - 3) = 10x^2 - 30x
\]
\[
-6x(x + 7) = -6x^2 - 42x
\]

Now, substitute these expressions back into the equation:

\[
(10x^2 - 30x) - (6x^2 + 42x)
\]

Simplify by combining like terms:

\[
10x^2 - 6x^2 = 4x^2
\]
\[
-30x - 42x = -72x
\]

Thus, the simplified form of the equation is:

\[
4x^2 - 72x
\]

We can factor this expression:

\[
4x(x - 18)
\]

This is the simplified answer: \( 4x(x - 18) \).

Would you like more details or have any questions about the process? Here are some related questions you can explore:

1. How do you factor quadratic equations?
2. What happens when \(x = 18\) in the solution?
3. How can we graph \( 4x(x - 18) \)?
4. What are the roots of the equation \( 4x(x - 18) = 0 \)?
5. How does distributing terms in algebra work in different cases?

**Tip:** Always check for common factors before expanding expressions—it can simplify your work!

Explore the step-by-step process of simplifying and factoring the expression 5x2 x(x-3) - 6x(x+7). This problem covers core algebra concepts, including the distributive property and factoring quadratic equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation