How do you solve an equation by factorising?

Answer 1

Let A and B be any number. Let's say you have (5-A)(10-B) = 0.

For this to be true, either (5-A) or (10-B) must be zero for the the answer to equal zero. Essentially what you are saying is 0(10-B)=0 or (10-A)0=0. This let's you solve for A and B.

You can just set each "factor" to zero and solve for the variable.

5-A=0

A=5

10-B=0

B=10

Another "un-factored" example:

x2 - 10x = -25

x2 - 10x + 25 = 0 <--- the factors have to be equal to zero for this to work

You need two numbers that add to negative 10 and multiply to 25.

(-5) + (-5) = -10

(-5) x (-5) = 25

Therefore:

(x-5)(x-5)=0

And x can only be equal to 5, x=5