<PRE><B>Question 169357</B>
32x^2+60x=27&lt;br&gt;

To solve this we need to get it so the equation is equal to 0 so we can use the zero product property so to do that we need to subtract 27 from both sides.&lt;br&gt;

32x^2+60x-27=0&lt;br&gt;

now we just factor this.  We need to multiply -27 and 32 together to get -864.  Now we need to list the factors of -864 to see if we can find factors that will add to 60. &lt;br&gt; 

1,864
2,432
3,288
4,216
6,144
8,108
9,96
12,72&lt;br&gt;

we can stop here because 72 + -12 = 60.  so now we write them into the equation.&lt;br&gt;

32x^2-12x+72x-27 = 0&lt;br&gt;

now we can just factor by grouping&lt;br&gt;

32x^2-12x+72x-27 = 0
4x(8x-3)+9(8x-3) = 0
(4x+9)(8x-3)=0&lt;br&gt;

now we can use the zero product property and set each factor equal to zero.&lt;br&gt;

4x+9 = 0 
4x = -9
x = -9/4&lt;br&gt;

8x-3 = 0
8x = 3
x = 3/8&lt;br&gt;

Now we should plug in our solutions to check them and I will leave that to you, you will find that these will work out.  </PRE>