Factorise the quadratic equation: x^2 + 5x + 6 = 0 and hence find the two solutions to the equation.

1. Start by writing the equation out again: x² + 5x + 6 = 0

2. I do it by thinking which two numbers add together to = 5 and which same two numbers multiply to = 6. The answer to this is 2 and 3.

3. So the next step is to write the eqaution down in factorised form (there is no need to do any other thinking about the numbers to go inside the brackets becuase the coefficient of x² is 1).

4. So we now have: (x + 2)(x + 3) = 0 - This is the answer to the first part of the question.

5. To get the answer to the second part, one of the two brackets must = 0 (because if two numbers multiplied together = 0, one number must = 0).

6. So either x + 2 = 0, in which case x = -2, or x + 3 = 0 in which case x = -3. This is the answer to the second part.

7.To check, substitute these number back into the original equation: (-2)² + 5(-2) + 6 = 4 - 10 + 6 = 0 (correct) (-3)² + 5(-3) + 6 = 9 - 15 + 6 = 0 (correct)