SOLUTION: Please help me solve this equation (sqrt6-6)(sqrt3+4)

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Question 614658: Please help me solve this equation (sqrt6-6)(sqrt3+4)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%286%29-6%29%28sqrt%283%29%2B4%29
First of all, this is not an equation. There is no equals sign. It is an expression. And expressions are simplified, not solved.

Just as with any pair of binomials (two-term expressions), you use FOIL to multiply:
F: sqrt%286%29%2Asqrt%283%29
Using the property of radicals, root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29, this becomes:
sqrt%286%2A3%29+=+sqrt%2818%29
And since 18 has a perfect square factor, sqrt%2818%29 will simplify:
sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2Asqrt%282%29+=+3sqrt%282%29

O: sqrt%286%29%2A4+=+4sqrt%286%29
I: -6%2Asqrt%283%29+=+-6sqrt%283%29
L: -6%2A4+=+-12

Putting this all together we get:

None of these terms are like terms so they cannot be added. This expression (or, if you prefer subtractions, 3sqrt%282%29+%2B+4sqrt%286%29+-6sqrt%283%29+-12) is the simplified expression.