Algebra Examples

Find the Roots (Zeros) -3x^2e^(-2x)+3xe^(-2x)
Step 1
Set equal to .
Step 2
Solve for .
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3
Set equal to .
Step 2.4
Set equal to and solve for .
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Step 2.4.1
Set equal to .
Step 2.4.2
Solve for .
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Step 2.4.2.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.4.2.2
The equation cannot be solved because is undefined.
Undefined
Step 2.4.2.3
There is no solution for
No solution
No solution
No solution
Step 2.5
Set equal to and solve for .
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Step 2.5.1
Set equal to .
Step 2.5.2
Solve for .
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Step 2.5.2.1
Subtract from both sides of the equation.
Step 2.5.2.2
Divide each term in by and simplify.
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Step 2.5.2.2.1
Divide each term in by .
Step 2.5.2.2.2
Simplify the left side.
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Step 2.5.2.2.2.1
Dividing two negative values results in a positive value.
Step 2.5.2.2.2.2
Divide by .
Step 2.5.2.2.3
Simplify the right side.
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Step 2.5.2.2.3.1
Divide by .
Step 2.6
The final solution is all the values that make true.
Step 3