Split the second term in \(3{x}^{2}-8x-16\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -16=-48\]
Ask: Which two numbers add up to \(-8\) and multiply to \(-48\)?
Split \(-8x\) as the sum of \(4x\) and \(-12x\).
\[3{x}^{2}+4x-12x-16\]
\[3{x}^{2}+4x-12x-16=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(3x+4)-4(3x+4)=0\]
Factor out the common term \(3x+4\).
\[(3x+4)(x-4)=0\]
Solve for \(x\).
Ask: When will \((3x+4)(x-4)\) equal zero?
When \(3x+4=0\) or \(x-4=0\)
Solve each of the 2 equations above.
\[x=-\frac{4}{3},4\]
\[x=-\frac{4}{3},4\]
Decimal Form: -1.333333, 4
x=-4/3,4
