Question

How do you solve `3x^2 = -9x`?

Answer 1

The two solutions are `x=0` and `x=-3`.

Explanation:

First, bring everything to one side of the equation:

`3x^2=-9x`

`3x^2color(blue)+color(blue)(9x)=-9xcolor(blue)+color(blue)(9x)`

`3x^2color(blue)+color(blue)(9x)=color(red)cancelcolor(black)(color(black)-9xcolor(blue)+color(blue)(9x))`

`3x^2+9x=0`

Now, divide by the common factor `3`:

`color(blue)(color(black)(3x^2+9x)/3)=color(blue)(color(black)0/3)`

`color(blue)(color(black)(color(red)cancelcolor(black)3x^2+color(red)cancelcolor(black)9^3x)/color(red)cancelcolor(blue)3)=color(blue)(color(black)0/3)`

`x^2+3x=color(blue)(color(black)0/3)`

`x^2+3x=0`

Now, use the distributive property backward to factor out the `x` term:

`color(red)x*color(blue)x+color(red)x*color(blue)3=0`

`(color(red)x)(color(blue)(x+3))=0`

Now, set each factor equal to `0` and solve for `x` in each one:

#color(white){color(black)( (color(red)x=0,qquadcolor(blue)(x+3)=0), (,qquadcolor(blue)x=-3):}#

These are the two solutions: `x=0` and `x=-3`. Hope this helped!