x² + 6x = 40 Subtract 40 on both sides to get the equation equal to 0.
x² + 6x - 40 = 0
Now you need to factor the equation. To do so, you find the factors of 40 that add or subtract to 6.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
[1 × 40, 2 × 20, 4 × 10, 5 × 8]
4 and 10 subtracts to 6.
Instead of 6x:
x² + 6x - 40 = 0
You can replace 6x with:
x² - 4x + 10x - 40 = 0 [this is because the sum of -4x and 10x is 6x]
Now factor the equation separately. Factor out x in (x² - 4x), and factor out 10 in (10x - 40)
x(x - 4) + 10(x - 4) = 0 Factor out (x - 4)
(x - 4)(x + 10) = 0
x - 4 = 0 Add 4 on both sides
x = 4
x + 10 = 0 Subtract 10 on both sides
x = -10
x = 4, x = -10