Find the solutions of
`x^(2)+x-12 = 0`

Answer

To solve the quadratic equation \(x^2 + x - 12 = 0\), we can use the method of factoring. Here are the steps:

### Step 1: Write down the equation
We start with the equation:
\[ x^2 + x - 12 = 0 \]

### Step 2: Factor the quadratic expression
We need to factor the expression \(x^2 + x - 12\). We look for two numbers that multiply to \(-12\) (the constant term) and add to \(1\) (the coefficient of \(x\)). The numbers that satisfy this are \(4\) and \(-3\).

So, we can rewrite the equation as:
\[ x^2 + 4x - 3x - 12 = 0 \]

### Step 3: Group the terms
Next, we group the terms:
\[ (x^2 + 4x) + (-3x - 12) = 0 \]

### Step 4: Factor by grouping
Now we factor out the common factors from each group:
\[ x(x + 4) - 3(x + 4) = 0 \]

### Step 5: Factor out the common binomial
We can now factor out the common binomial \((x + 4)\):
\[ (x + 4)(x - 3) = 0 \]

### Step 6: Set each factor to zero
Now we set each factor equal to zero:
1. \(x + 4 = 0\)
2. \(x - 3 = 0\)

### Step 7: Solve for \(x\)
Solving these equations gives us:
1. \(x = -4\)
2. \(x = 3\)

### Conclusion
The solutions to the equation \(x^2 + x - 12 = 0\) are:
\[ x = -4 \quad \text{and} \quad x = 3 \]

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