Solve by factoring (no "c" term-GCF): -2x^2+6x=0

Question

Please explain each step. There can be 2 answers.

Answer 1

-2x^2 +6x = 0

divide by -2x

-2x(x-3) = 0

x-3 =0

x=3

-2x=0

x =0 is the other solution

Answer 2

Hi Alia, I can offer assistance on this problem, because it is slightly different than the problem I assisted with previously. Here, instead of there being an equation like before where we have "ax^2 + bx + c = 0" we now have "ax^2 + bx = 0." Hence, the no "c" term as stated in the problem.

1.) Start by making sure everything is on one side of the equation. Here we already have all of the terms on the left side of the equation.

2.) Next, you will want to factor -2x^2 + 6x = 0. Notice how you can factor out a -2x: -2x(x - 3) = 0. Thus, our new factored equation becomes: -2x(x - 3) = 0. A good way to check that you have factored correctly is to expand and see if you get the same equation as the one before our factoring. -2x(x - 3) = 0 is equal to -2x^2 - 2x*(-3) = -2x^2 + 6x = 0. The equation -2x^2 + 6x = 0 is indeed the same equation as the one before our factoring. We have factored correctly.

3.) Now that we have factored, you want to set each factor equal to 0: -2x = 0 and x - 3 = 0. The first equation implies that x = 0. For the second equation, we get x = 3.

Hence, the solutions to the equation -2x^2 + 6x = 0 are x = 0 and x = 3.

I will leave it up to you to verify that these are in fact solutions (i.e. plug each value into our original equation and see if you get 0).