Question 169357: Solve 32x^2+60x=27
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! 32x^2+60x=27
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.
32x^2+60x-27=0
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.
1,864
2,432
3,288
4,216
6,144
8,108
9,96
12,72
we can stop here because 72 + -12 = 60. so now we write them into the equation.
32x^2-12x+72x-27 = 0
now we can just factor by grouping
32x^2-12x+72x-27 = 0
4x(8x-3)+9(8x-3) = 0
(4x+9)(8x-3)=0
now we can use the zero product property and set each factor equal to zero.
4x+9 = 0
4x = -9
x = -9/4
8x-3 = 0
8x = 3
x = 3/8
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.
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