Split the second term in \(2{x}^{2}-x-3\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[2\times -3=-6\]
Ask: Which two numbers add up to \(-1\) and multiply to \(-6\)?
Split \(-x\) as the sum of \(2x\) and \(-3x\).
\[2{x}^{2}+2x-3x-3\]
\[2{x}^{2}+2x-3x-3=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[2x(x+1)-3(x+1)=0\]
Factor out the common term \(x+1\).
\[(x+1)(2x-3)=0\]
Solve for \(x\).
Ask: When will \((x+1)(2x-3)\) equal zero?
When \(x+1=0\) or \(2x-3=0\)
Solve each of the 2 equations above.
\[x=-1,\frac{3}{2}\]
\[x=-1,\frac{3}{2}\]
Decimal Form: -1, 1.5
x=-1,3/2
