Question

Solve the equation by factoring.
2​x(xminus3​)equals8xsquaredminus7x

Answer 1

To solve the equation \( 2x(x - 3) = 8x^2 - 7x \) by factoring, we will first rearrange the equation to one side:

1. **Expand the left-hand side:**
\[
2x(x - 3) = 2x^2 - 6x
\]

2. **Set the equation to zero:**
\[
2x^2 - 6x = 8x^2 - 7x
\]
Subtract \( 8x^2 - 7x \) from both sides:
\[
2x^2 - 6x - 8x^2 + 7x = 0
\]
Combine like terms:
\[
-6x^2 + x = 0
\]

3. **Factor out the common term:**
\[
x(-6x + 1) = 0
\]

4. **Set each factor to zero:**
The first factor gives us:
\[
x = 0
\]
The second factor gives:
\[
-6x + 1 = 0 \implies 6x = 1 \implies x = \frac{1}{6}
\]

5. **Final solution:**
The solutions to the equation \( 2x(x - 3) = 8x^2 - 7x \) are:
\[
x = 0 \quad \text{and} \quad x = \frac{1}{6}
\]