Split the second term in \(3{x}^{2}-4x+1\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times 1=3\]
Ask: Which two numbers add up to \(-4\) and multiply to \(3\)?
Split \(-4x\) as the sum of \(-x\) and \(-3x\).
\[3{x}^{2}-x-3x+1\]
\[3{x}^{2}-x-3x+1=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(3x-1)-(3x-1)=0\]
Factor out the common term \(3x-1\).
\[(3x-1)(x-1)=0\]
Solve for \(x\).
Ask: When will \((3x-1)(x-1)\) equal zero?
When \(3x-1=0\) or \(x-1=0\)
Solve each of the 2 equations above.
\[x=\frac{1}{3},1\]
\[x=\frac{1}{3},1\]
Decimal Form: 0.333333, 1
x=1/3,1
