Question 73947
<pre><font size = 4><b>how do you solve 3x<sup>2</sup> - 5x = 8? 

3x² - 5x = 8

This is a quadratic equation. 

1. Get zero on the right by adding -8 to both sides

3x² - 5x - 8 = 0

2. Ignore the signs and multiply the 3 by the 8, getting 24

Think of two whole numbers whose product in 15 and whose

DIFFERENCE is 5. (DIFFERENCE because of the sign before the
 8 is - . If it had been + I would have said "SUM")

A little thinking gives us 8 and 3, because

8×3 = 24 and 8-3 = 5

Rewrite the 5 as (8-3)

3x² - (8-3)x - 8 = 0

Remove the parentheses

3x² - 8x + 3x - 5 = 0

Factor x out of the first two terms

x(3x - 8) + 3x - 5 = 0

Factor 1 out of the last two terms:
(Note: if you can't factor anything else 
out of one of the pair of terms, factor 
out 1 or -1.)

x(3x - 8) + 1(3x - 8) = 0

Now I'll do some coloring to help
you see what I'm doing:

<font color = "blue">x</font><font color = "red">(3x - 8)</font> <font color = "blue">+ 1</font><font color = "red">(3x - 8)</font> = 0

Now factor out the red <font color = "red">(3x - 8)</font>,
putting the blue <font color = "blue">x</font> and the blue <font color = "blue">+ 1</font> inside parentheses

<font color = "red">(3x - 8)</font>(<font color = "blue">x + 1</font>) = 0

Set each factor = 0 and solve for x

<font color = "red">3x - 8</font> = 0           <font color = "blue">x + 1</font> = 0
    3x = 8               x = -1
     x = 8/3

Edwin </pre>