Question

solve the equation by factoring: 6x^2 = 1-x ?

Answer 1

Subtract one from each side. Add x to each side.

Answer 2

What is the new equation?

Answer 3

@jojor_124

Answer 4

Subtract 1 from both sides.
Add x to both sides.
You now have: \[6x^2+x-1\]
What two numbers multiply together to equal 6? 3 and 2, 6 and 1. You know that the correct numbers to factor are 3 and 2 because 6*1=6 and there's no way you could subtract 5 to get your desired "+x" part of the puzzle.
What numbers multiply together to equal -1? 1, -1. Thus, one parenthesis must be -1 and the other must be +1.
So there are only 2 possible solutions at this point:
(3x-1)(2x+1) OR (3x+1)(2x-1)
Multiply the first one out, and you are left with:
\[6x^2+x-1\]
which is your original equation! Thus, the answer is (3x-1)(2x+1)