Multiply both sides by \(x\).
\[3{x}^{2}+2=7x\]
Move all terms to one side.
\[3{x}^{2}+2-7x=0\]
Split the second term in \(3{x}^{2}+2-7x\) 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 \(-7\) and multiply to \(6\)?
Split \(-7x\) as the sum of \(-x\) and \(-6x\).
\[3{x}^{2}-x-6x+2\]
\[3{x}^{2}-x-6x+2=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(3x-1)-2(3x-1)=0\]
Factor out the common term \(3x-1\).
\[(3x-1)(x-2)=0\]
Solve for \(x\).
Ask: When will \((3x-1)(x-2)\) equal zero?
When \(3x-1=0\) or \(x-2=0\)
Solve each of the 2 equations above.
\[x=\frac{1}{3},2\]
\[x=\frac{1}{3},2\]
Decimal Form: 0.333333, 2
x=1/3,2
