SOLUTION: How to solve equations by factoring?

Question 1009206: How to solve equations by factoring?

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The most fundamental tools for solving equations are addition, subtraction, multiplication, and division. These methods work well for equations like:
and
But what about equations where the variable carries an exponent, like ? This is where comes in.
The Solve by Factoring process will require four major steps:
Move all terms to one side of the equation, usually the left, using addition or subtraction.
Factor the equation completely.
Set each factor equal to zero, and solve.
List each solution from Step 3 as a solution to the original equation.
Example:

Step 1
The first step is to

to the using addition and subtraction. First, we will subtract from each side.

Now, we will add to each side.

With all terms on the side, we proceed to
Step 2
We identify the left as a trinomial, and factor it accordingly:
.......write as
......group

We now have two factors, and .
Step 3
We now set each factor to . The result is two subproblems:

and

Solving the first subproblem, , gives . Solving the second subproblem, , gives .
Step 4
The final step is to combine the two previous solutions, and , into one solution for the original problem.

=,

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