Factor out the common term \(x\).
\[\frac{x(x-3)}{7}+x=11\]
Multiply both sides by \(7\).
\[x(x-3)+7x=77\]
Expand.
\[{x}^{2}-3x+7x=77\]
Simplify \({x}^{2}-3x+7x\) to \({x}^{2}+4x\).
\[{x}^{2}+4x=77\]
Move all terms to one side.
\[{x}^{2}+4x-77=0\]
Factor \({x}^{2}+4x-77\).
Ask: Which two numbers add up to \(4\) and multiply to \(-77\)?
Rewrite the expression using the above.
\[(x-7)(x+11)\]
\[(x-7)(x+11)=0\]
Solve for \(x\).
Ask: When will \((x-7)(x+11)\) equal zero?
When \(x-7=0\) or \(x+11=0\)
Solve each of the 2 equations above.
\[x=7,-11\]
\[x=7,-11\]
x=7,-11
