So to find the solutions, I will be factoring by grouping. Firstly, what two terms have a product of 12x² and a sum of -8x? That would be -2x and -6x. Replace -8x with -2x - 6x:
[tex]4x^2-2x-6x+3=0[/tex]
Next, factor 4x² - 2x and -6x + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:
[tex]2x(2x-1)-3(2x-1)=0[/tex]
Now you can rewrite it as:
[tex](2x-3)(2x-1)=0[/tex]
Now, apply the zero product property and solve:
[tex]2x-3=0\\2x=3\\x=\frac{3}{2}\ \textsf{OR}\ 1.5\\\\2x-1=0\\2x=1\\x=\frac{1}{2}\ \textsf{OR}\ 0.5[/tex]
In short, x = 3/2 (1.5) and 1/2 (0.5).
