SOLUTION: How do you solve: 4h(3h + 2) = h + 12 Thank you!

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Question 292499: How do you solve:
4h(3h + 2) = h + 12

Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4h%283h+%2B+2%29+=+h+%2B+12 Start with the given equation.


12h%5E2%2B8h+=+h+%2B+12 Distribute


12h%5E2%2B8h+-+h+-+12+=+0 Get everything to one side.


12h%5E2%2B7h+-+12+=+0 Combine like terms.


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for h:


Starting with the general quadratic


ah%5E2%2Bbh%2Bc=0


the general solution using the quadratic equation is:


h+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 12%2Ah%5E2%2B7%2Ah-12=0 ( notice a=12, b=7, and c=-12)





h+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A12%2A-12+%29%29%2F%282%2A12%29 Plug in a=12, b=7, and c=-12




h+=+%28-7+%2B-+sqrt%28+49-4%2A12%2A-12+%29%29%2F%282%2A12%29 Square 7 to get 49




h+=+%28-7+%2B-+sqrt%28+49%2B576+%29%29%2F%282%2A12%29 Multiply -4%2A-12%2A12 to get 576




h+=+%28-7+%2B-+sqrt%28+625+%29%29%2F%282%2A12%29 Combine like terms in the radicand (everything under the square root)




h+=+%28-7+%2B-+25%29%2F%282%2A12%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




h+=+%28-7+%2B-+25%29%2F24 Multiply 2 and 12 to get 24


So now the expression breaks down into two parts


h+=+%28-7+%2B+25%29%2F24 or h+=+%28-7+-+25%29%2F24


Lets look at the first part:


x=%28-7+%2B+25%29%2F24


h=18%2F24 Add the terms in the numerator

h=3%2F4 Divide


So one answer is

h=3%2F4




Now lets look at the second part:


x=%28-7+-+25%29%2F24


h=-32%2F24 Subtract the terms in the numerator

h=-4%2F3 Divide


So another answer is

h=-4%2F3


So our solutions are:

h=3%2F4 or h=-4%2F3