# Algebra Examples

,
Step 1
Subtract from both sides of the equation.
Step 2
Factor by grouping.
Step 2.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Step 2.1.1
Multiply by .
Step 2.1.2
Rewrite as plus
Step 2.1.3
Apply the distributive property.
Step 2.2
Factor out the greatest common factor from each group.
Step 2.2.1
Group the first two terms and the last two terms.
Step 2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4
Set equal to and solve for .
Step 4.1
Set equal to .
Step 4.2
Solve for .
Step 4.2.1
Add to both sides of the equation.
Step 4.2.2
Divide each term in by and simplify.
Step 4.2.2.1
Divide each term in by .
Step 4.2.2.2
Simplify the left side.
Step 4.2.2.2.1
Cancel the common factor of .
Step 4.2.2.2.1.1
Cancel the common factor.
Step 4.2.2.2.1.2
Divide by .
Step 5
Set equal to and solve for .
Step 5.1
Set equal to .
Step 5.2
Subtract from both sides of the equation.
Step 6
The final solution is all the values that make true.
Step 7
Find the values of that produce a value within the interval .
Step 7.1
The interval does not contain . It is not part of the final solution.
is not on the interval
Step 7.2
The interval contains .