Split the second term in \(6{X}^{2}-5X+1\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[6\times 1=6\]
Ask: Which two numbers add up to \(-5\) and multiply to \(6\)?
Split \(-5X\) as the sum of \(-2X\) and \(-3X\).
\[6{X}^{2}-2X-3X+1\]
\[6{X}^{2}-2X-3X+1=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[2X(3X-1)-(3X-1)=0\]
Factor out the common term \(3X-1\).
\[(3X-1)(2X-1)=0\]
Solve for \(X\).
Ask: When will \((3X-1)(2X-1)\) equal zero?
When \(3X-1=0\) or \(2X-1=0\)
Solve each of the 2 equations above.
\[X=\frac{1}{3},\frac{1}{2}\]
\[X=\frac{1}{3},\frac{1}{2}\]
Decimal Form: 0.333333, 0.5
X=1/3,1/2
