The problem is to solve the quadratic equation $x^2 + 3x = -2(-3-x)$.

1. Problem Description

The problem is to solve the quadratic equation $x^2 + 3x = -2(-3-x)$.

2. Solution Steps

First, expand the right side of the equation:

$x^2 + 3x = -2(-3) - 2(-x)$

$x^2 + 3x = 6 + 2x$

Next, move all terms to one side to set the equation equal to zero:

$x^2 + 3x - 2x - 6 = 0$

$x^2 + x - 6 = 0$

Now, factor the quadratic equation:

$(x + 3)(x - 2) = 0$

Set each factor equal to zero and solve for $x$:

$x + 3 = 0$ or $x - 2 = 0$

$x = -3$ or $x = 2$

3. Final Answer

$x = -3, 2$