Move all terms to one side.
\[8{q}^{2}+6q-5=0\]
Split the second term in \(8{q}^{2}+6q-5\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[8\times -5=-40\]
Ask: Which two numbers add up to \(6\) and multiply to \(-40\)?
Split \(6q\) as the sum of \(10q\) and \(-4q\).
\[8{q}^{2}+10q-4q-5\]
\[8{q}^{2}+10q-4q-5=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[2q(4q+5)-(4q+5)=0\]
Factor out the common term \(4q+5\).
\[(4q+5)(2q-1)=0\]
Solve for \(q\).
Ask: When will \((4q+5)(2q-1)\) equal zero?
When \(4q+5=0\) or \(2q-1=0\)
Solve each of the 2 equations above.
\[q=-\frac{5}{4},\frac{1}{2}\]
\[q=-\frac{5}{4},\frac{1}{2}\]
Decimal Form: -1.25, 0.5
q=-5/4,1/2
