we have
\(8x^2+13x - 6\)
Equate the function to zero
\(8x^2+13x - 6=0\)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(8x^2+13x = 6\)
Factor the leading coefficient
\(8(x^2+\frac{13}{8}x) = 6\)
Complete the square. Remember to balance the equation by adding the same constants to each side.
\(8(x^2+\frac{13}{8}x) = 6\)
\(8(x^2+\frac{13}{8}x+\frac{169}{256}) = 6 +\frac{169}{32} \\ \\ 8(x+\frac{13}{16} )^{2} =\frac{361}{32} \\ \\ (x+\frac{13}{16} )^{2} =\frac{361}{256}\\ \\ (x+\frac{13}{16} ) =(+/-)\sqrt{\frac{361}{256}} \\ \\ (x+\frac{13}{16} ) =(+/-)\frac{19}{16} \\ \\ x1=-\frac{13}{16} +\frac{19}{16} =\frac{6}{16}\\ \\ x2=-\frac{13}{16} -\frac{19}{16}=-2\)
the factorization is equal to
\(8*(x-\frac{6}{16} )*(x+2)=(8x-3)*(x+2)\)
therefore
the answer is
\((8x-3)*(x+2)\)
