Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{3}^{{x}^{2}+2x}={3}^{15}\]
Cancel the base of \(3\) on both sides.
\[{x}^{2}+2x=15\]
Move all terms to one side.
\[{x}^{2}+2x-15=0\]
Factor \({x}^{2}+2x-15\).
Ask: Which two numbers add up to \(2\) and multiply to \(-15\)?
Rewrite the expression using the above.
\[(x-3)(x+5)\]
\[(x-3)(x+5)=0\]
Solve for \(x\).
Ask: When will \((x-3)(x+5)\) equal zero?
When \(x-3=0\) or \(x+5=0\)
Solve each of the 2 equations above.
\[x=3,-5\]
\[x=3,-5\]
x=3,-5
