x = [tex]\frac{1}{2}[/tex] or x = - [tex]\frac{4}{3}[/tex]
consider the factors of the product 6 × - 4 = - 24 which sum to the coefficient of the x- term ( + 5)
the factors are + 8 and - 3 ( split the middle term using these factors
6x² - 3x + 8x - 4 = 0 ( factor by grouping )
3x(2x - 1) + 4(2x - 1 ) ( take out common factor of (2x - 1) )
= (2x - 1)(3x + 4) = 0
equate each factor to zero and solve for x
2x - 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]
3x + 4 = 0 ⇒ x = - [tex]\frac{4}{3}[/tex]
6x² + 5x - 4 = 0
Multiply the first and last term (6x² * -4) to get -24x². Now find two factors of -24x² whose sum is the middle term (5x). -3x + 8x Replace 5x with -3x + 8x, then factor and solve.
6x² - 3x + 8x - 4 = 0
3x(2x - 1) +4(2x - 1) = 0
(3x + 4) (2x - 1) = 0
3x + 4 = 0 or 2x - 1 = 0
x = [tex]-\frac{4}{3}[/tex] or x = [tex]\frac{1}{2}[/tex]
Note: you can also use the quadratic formula to find the foots.
