Solve the quadratic equation by factoring x²-5x=2x²+x

To solve the quadratic equation \( x^2 - 5x = 2x^2 + x \) by factoring, follow these steps:

### Step 1: Rearrange the equation
Move all terms to one side of the equation to set it equal to zero.

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

Combine like terms:

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

### Step 2: Factor the equation
Factor out the common factor, which is \(-x\):

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

### Step 3: Solve for \(x\)
Set each factor equal to zero:

1. \(-x = 0\) gives \( x = 0 \)
2. \(x + 6 = 0\) gives \( x = -6 \)

### Final Answer:
The solutions to the equation are \( x = 0 \) and \( x = -6 \).

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

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Here are 5 related questions for further practice:

1. Solve the quadratic equation by factoring: \( x^2 + 7x + 10 = 0 \).
2. Factor and solve the equation: \( 3x^2 - 12x = 0 \).
3. Solve \( 2x^2 - 4x = 0 \) by factoring.
4. How do you factor the quadratic equation \( x^2 - 4x - 12 = 0 \)?
5. What are the solutions to \( x^2 + 5x + 6 = 0 \)?

**Tip:** Always start by rearranging the equation so that all terms are on one side before attempting to factor.

Learn how to solve the quadratic equation x^2 - 5x = 2x^2 + x step-by-step with detailed explanations. This problem involves rearranging terms, factoring, and solving for x. Suitable for students in Grades 7-9.

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