Question

How do you factor and solve `3x^2+ 2x = 8`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(8)` from each side of the equation to put in standard quadratic form:

`3x^2 + 2x - color(red)(8) = 8 - color(red)(8)`

`3x^2 + 2x - 8 = 0`

Next, playing with factors of 3 (1 x 3 and 3 x 1) and factors of 8 (1 x 8, 2 x 4, 4 x 2 and 8 x 1) we can factor this as:

`(3x - 4)(x + 2) = 0`

Now, solve each term for `0`:

Solution 1)

`3x - 4 = 0`

`3x - 4 + color(red)(4) = 0 + color(red)(4)`

`3x - 0 = 4`

`3x = 4`

`(3x)/color(red)(3) = 4/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 4/3`

`x = 4/3`

Solution 2)

`x + 2 = 0`

`x + 2 - color(red)(2) = 0 - color(red)(2)`

`x + 0 = -2`

`x = -2`

The solution is: `x = 4/3` and `x = -2`