Using the factoring​ method, solve for the roots of the quadratic equation. Be sure to place your equation in standard form before factoring.3 x squared minus x equals negative 7 xQuestion content area bottomPart 1xequalsenter your response here ​(Simplify your answer. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation using the factoring method, we first need to write the equation in standard form, which is \( ax^2 + bx + c = 0 \).

Given the equation:

\[ 3x^2 - x = -7x \]

We start by moving all terms to one side of the equation:

\[ 3x^2 - x + 7x = 0 \]

Combining like terms gives us:

\[ 3x^2 + 6x = 0 \]

Now, we can factor out the greatest common factor (GCF):

\[ 3x(x + 2) = 0 \]

Now, we can set each factor equal to zero:

1. \( 3x = 0 \)
2. \( x + 2 = 0 \)

Solving these equations:

1. From \( 3x = 0 \): \[ x = 0 \]

2. From \( x + 2 = 0 \): \[ x = -2 \]

Therefore, the roots of the quadratic equation are:

\[ x = 0, -2 \]

So the final answer is:

\[ \boxed{0, -2} \]