Split the second term in \(3{x}^{2}-4x-7\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -7=-21\]
Ask: Which two numbers add up to \(-4\) and multiply to \(-21\)?
Split \(-4x\) as the sum of \(3x\) and \(-7x\).
\[3{x}^{2}+3x-7x-7\]
\[3{x}^{2}+3x-7x-7=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[3x(x+1)-7(x+1)=0\]
Factor out the common term \(x+1\).
\[(x+1)(3x-7)=0\]
Solve for \(x\).
Ask: When will \((x+1)(3x-7)\) equal zero?
When \(x+1=0\) or \(3x-7=0\)
Solve each of the 2 equations above.
\[x=-1,\frac{7}{3}\]
\[x=-1,\frac{7}{3}\]
Decimal Form: -1, 2.333333
x=-1,7/3
