Factor out the common term \(x\).
\[\frac{x(x+4)}{4}=\frac{6+x}{8}+\frac{14+x}{8}\]
Join the denominators.
\[\frac{x(x+4)}{4}=\frac{6+x+14+x}{8}\]
Simplify \(6+x+14+x\) to \(20+2x\).
\[\frac{x(x+4)}{4}=\frac{20+2x}{8}\]
Factor out the common term \(2\).
\[\frac{x(x+4)}{4}=\frac{2(10+x)}{8}\]
Simplify \(\frac{2(10+x)}{8}\) to \(\frac{10+x}{4}\).
\[\frac{x(x+4)}{4}=\frac{10+x}{4}\]
Multiply both sides by \(4\).
\[x(x+4)=10+x\]
Expand.
\[{x}^{2}+4x=10+x\]
Move all terms to one side.
\[{x}^{2}+4x-10-x=0\]
Simplify \({x}^{2}+4x-10-x\) to \({x}^{2}+3x-10\).
\[{x}^{2}+3x-10=0\]
Factor \({x}^{2}+3x-10\).
Ask: Which two numbers add up to \(3\) and multiply to \(-10\)?
Rewrite the expression using the above.
\[(x-2)(x+5)\]
\[(x-2)(x+5)=0\]
Solve for \(x\).
Ask: When will \((x-2)(x+5)\) equal zero?
When \(x-2=0\) or \(x+5=0\)
Solve each of the 2 equations above.
\[x=2,-5\]
\[x=2,-5\]
x=2,-5
