Question

Use factoring to solve quadratic equation. Check by substitution or by a graphing utility.

Answer 1

Start by moving all terms to left side of equation 4x^2 - 19x - 30 = 0
Multiply 4 x -30 = -120
Now find two factors of 120 that subtract to give 19... 1 x 120, 2 x 60, 3 x 40, 4 x 30, 5 x 24 ✅
[if it had been +120 we would add the factors looking for 19 which in this case don’t exist]
To get -19 we will need 5 + -24
24 is a multiple of 4 so we can use 4 x -6 and 1 x 5
Giving a factored equation of (4x + 5)(x - 6) = 0 [you should check this by expanding to remove the brackets]

One of the brackets must = zero so the solutions are x = -5/4 or x = 6

Some people look at factors of 4 and -30 and then pair then up to find a sum of -19 but this can take longer to finish.