solve by factoring: $x^{2}+x = 30$

Explanation:

Step1: Rearrange to standard form

$x^{2}+x - 30=0$

Step2: Factor the quadratic

We need two numbers that multiply to -30 and add up to 1. The numbers are 6 and - 5. So, $(x + 6)(x - 5)=0$

Step3: Set each factor equal to zero

$x+6 = 0$ or $x - 5=0$

Step4: Solve for x

For $x+6 = 0$, we get $x=-6$. For $x - 5=0$, we get $x = 5$

Answer:

$x=-6, x = 5$