# Solve for x e^(2x)-3e^x+2=0 Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Replace the left side with the factored expression.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
Expand by moving outside the logarithm.
The natural logarithm of is .
Multiply by .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
Expand by moving outside the logarithm.
The natural logarithm of is .
Multiply by .
The natural logarithm of is .
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for x e^(2x)-3e^x+2=0     