Split the second term in \(3{x}^{2}+x-2\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -2=-6\]
Ask: Which two numbers add up to \(1\) and multiply to \(-6\)?
Split \(x\) as the sum of \(3x\) and \(-2x\).
\[3{x}^{2}+3x-2x-2\]
\[3{x}^{2}+3x-2x-2=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[3x(x+1)-2(x+1)=0\]
Factor out the common term \(x+1\).
\[(x+1)(3x-2)=0\]
Solve for \(x\).
Ask: When will \((x+1)(3x-2)\) equal zero?
When \(x+1=0\) or \(3x-2=0\)
Solve each of the 2 equations above.
\[x=-1,\frac{2}{3}\]
\[x=-1,\frac{2}{3}\]
Decimal Form: -1, 0.666667
x=-1,2/3
