Solve the equation: `x^{2}+x-42\ =\ 0\ `for x by FACTORING.
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To solve this equation by factoring, we need to find two numbers that multiply to give us -42 and add to give us +1.
The factors of -42 are:
1, -42
2, -21
3, -14
6, -7
Out of these factors, the pair that adds to give us +1 is 6 and -7.
We can rewrite the equation as:
(x + 6)(x - 7) = 0
Setting each factor equal to 0 and solving for x, we get:
x + 6 = 0 -> x = -6
x - 7 = 0 -> x = 7
Therefore, the solutions to the equation x^2 + x - 42 = 0 are x = -6 and x = 7.