The answer is -(5x-4)(4x+3)
Factor out a negative from the entire expression
−20x² + x + 12
= −(20x² - x - 12)
Find two numbers so that they
⇒ Multiply to get 20 * -12 = -240
⇒ and add to get -1 (coefficient on x term)
These two numbers are -16 and 15 (not very obvious; might have to crunch some numbers)
We can break down the x term using -16 and 15 as coefficients on x
−(20x² - x - 12)
= −(20x² - 16x + 15x - 12)
We factor by grouping. Factor 4x out of 20x² - 16x and 3 out of 15x - 12 to get
= −[ 4x(5x - 4) + 3(5x - 4) ]
Factor out (5x-4) to get
= -(5x-4)[4x + 3]
= -(5x-4)(4x+3)