Move all terms to one side.
\[13x-21-2{x}^{2}=0\]
Multiply both sides by \(-1\).
\[2{x}^{2}-13x+21=0\]
Split the second term in \(2{x}^{2}-13x+21\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[2\times 21=42\]
Ask: Which two numbers add up to \(-13\) and multiply to \(42\)?
Split \(-13x\) as the sum of \(-6x\) and \(-7x\).
\[2{x}^{2}-6x-7x+21\]
\[2{x}^{2}-6x-7x+21=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[2x(x-3)-7(x-3)=0\]
Factor out the common term \(x-3\).
\[(x-3)(2x-7)=0\]
Solve for \(x\).
Ask: When will \((x-3)(2x-7)\) equal zero?
When \(x-3=0\) or \(2x-7=0\)
Solve each of the 2 equations above.
\[x=3,\frac{7}{2}\]
\[x=3,\frac{7}{2}\]
Decimal Form: 3, 3.5
x=3,7/2
