While this question may appear unfamiliar at first, it is just a quadratic equation in disguise. Rearranging such that it equals 0:
x^2 + 5x - 36 = 0
Now this equation is ready to be solved! We can approach this in a couple of ways. I'll go through the factorisation method and using the quadratic formula.
Factorisation Method
This method is often the quickest way but requires a bit of practise to be able to spot the solution. If we look at a general factorisation where the coefficient of x is 1 in both brackets, i.e.
(x+a)(x+b) = 0
We can see when we expand this, we get
x^2 + ax + bx + ab = 0
x^2 + (a+b)x + ab = 0
Going back to our example, this shows us that we need to think of numbers such that a + b = 5 and ab = -36. The tricky part is actually thinking of these numbers.
Because we know that ab is a negative number, we know either a or b must be negative because a negative times a positive is a negative. We now need to trial and error a few potential numbers to find our answers. With a bit of good guessing we can see that a = -4 and b = 9 will work because -4x9 = -36 and -4+9 = 5.
This gives us
(x-4)(x+9)=0
For this to equal zero, one of these brackets must equal 0. If the first one equals 0 then,
x-4 = 0
x=4
or the second one,
x+9=0
x=-9
So our answer is x=4 or x=-9.
If you found it difficult to guess the right numbers then keep practising but, in the meantime, the formula method always works without guessing but does take a little longer...
Formula Method
For a general quadration equation ax^2 + bx + c = 0, the quadratic formula is given by
x = (-b +/- sqrt(b^2 - 4ac))/2a
For our example, a = 1, b = 5 and c = -36, so:
x = (-5 +/- sqrt(25 + (4x36)))/2
x = (-5 +/- sqrt(25+144))/2
x = (-5 +/- sqrt(169))/2
x = (-5 +/- 13)/2
Taking the + option:
x = (-5 + 13)/2
x = 8/2
x = 4
Taking the - option:
x = (-5-13)/2
x = -18/2
x = -9
Therefore, x=4 or x=-9 as expected from our first method.