In this video, we are going to look at solving equations by factoring.To solve equations by factoring, we must make sure that the quadratic is set equal to 0.

For example:

If we are given the equation

we can first factor like normal. We need two numbers that add up to 5 and multiply to 6. These two numbers are 2 and 3. So we are left with

Now if we think about this logically, for two numbers to multiply together to give us 0, then at least one of these numbers must be 0. This means that either x+2 must equal 0 or x+3 must equal 0. So if we set each equal to 0 we get

and

When we solve both of these by simply subtracting 2 and subtracting 3, we get that

If we had something more complicated like

then the first step would be to subtract the 14 from both sides to make sure that our equation is set equal to 0. So now we are left with

From here we can factor and solve. Two numbers that add up to 3 and multiply to -10 are 5 and -2, so

From here, we set each factor equal to 0

and

and solve by subtracting 5 and adding 2 to get

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