Question

How do you solve `4x^2+6x=0` by factoring?

Answer 1

`x=0, -3/2`

Explanation:

Notice that we can factor out `2x` from both terms on the LH side:

`2x(2x+3)=0`

`:. 2x=0, 2x+3=0`

For `2x=0=>color(blue)(bar(ul(abs(color(black)(x=0`

For `2x+3=0`

`2x=-3=>color(blue)(bar(ul(abs(color(black)(x=-3/2`

We can see these in the graph:

graph{4x^2+6x}

Answer 2

`x=0`, `-3/2`

Explanation:

Solve:

`4x^2+6x=0`

The greatest common factor of `4` and `6` is `2`. The greatest common factor of `x^2` and `x` is `x`. The greatest common factor is `2x`. Factor out `2x`.

`2x(2x+3)=0`

`2x=0`

`x=0/2`

`x=0`

`2x+3=0`

`2x=-3`

`x=-3/2`

Solutions for `x`.

`x=0`, `-3/2`