Multiply both sides by \(-1\).
\[3{x}^{2}-x-4=0\]
Split the second term in \(3{x}^{2}-x-4\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -4=-12\]
Ask: Which two numbers add up to \(-1\) and multiply to \(-12\)?
Split \(-x\) as the sum of \(3x\) and \(-4x\).
\[3{x}^{2}+3x-4x-4\]
\[3{x}^{2}+3x-4x-4=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[3x(x+1)-4(x+1)=0\]
Factor out the common term \(x+1\).
\[(x+1)(3x-4)=0\]
Solve for \(x\).
Ask: When will \((x+1)(3x-4)\) equal zero?
When \(x+1=0\) or \(3x-4=0\)
Solve each of the 2 equations above.
\[x=-1,\frac{4}{3}\]
\[x=-1,\frac{4}{3}\]
Decimal Form: -1, 1.333333
x=-1,4/3
