Split the second term in \(3{g}^{2}-17g-6\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -6=-18\]
Ask: Which two numbers add up to \(-17\) and multiply to \(-18\)?
Split \(-17g\) as the sum of \(g\) and \(-18g\).
\[3{g}^{2}+g-18g-6\]
\[3{g}^{2}+g-18g-6=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[g(3g+1)-6(3g+1)=0\]
Factor out the common term \(3g+1\).
\[(3g+1)(g-6)=0\]
Solve for \(g\).
Ask: When will \((3g+1)(g-6)\) equal zero?
When \(3g+1=0\) or \(g-6=0\)
Solve each of the 2 equations above.
\[g=-\frac{1}{3},6\]
\[g=-\frac{1}{3},6\]
Decimal Form: -0.333333, 6
g=-1/3,6
