First, we need to convert this to the normal form of a quadratic equation:
#24x^2 - 6 - color(red)(10x)= 10x - color(red)(10x)#
#24x^2 - 10x - 6 = 0#
Next to factor the quadratic we need to play with multiplies for 24 (1x24, 2x12, 3x8, 4x6) and multipliers for 6 (1x6, 2x3) to give us:
#(4x - 3)(6x + 2) = 0#
We can now solve each term for #0#:
Solution 1)
#4x - 3 = 0#
#4x - 3 + color(red)(3) = 0 + color(red)(3)#
#4x - 0 = 3#
#4x = 3#
#(4x)/color(red)(4) = 3/color(red)(4)#
#(color(red)(cancel(color(black)(4)))x)/color(red)(cancel(color(black)(4))) = 3/4#
#x = 3/4#
Solution 2)
#6x + 2 = 0#
#6x + 2 - color(red)(2) = 0 - color(red)(2)#
#6x + 0 = -2#
#6x = -2#
#(6x)/color(red)(6) = -2/color(red)(6)#
#(color(red)(cancel(color(black)(6)))x)/color(red)(cancel(color(black)(6))) = -1/3#
#x = -1/3#
