Simplify: High School level Algebra question

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Simplify: High School level Algebra question

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[5(x^2-4)-(x^2-4)e ^{7-x}\]
oh goodness! I'm not that far yet! sorry!
The next step where I am stuck at is getting it to: \[(x^2-4)(5-e ^{7x})=0\]
I know what the final answer is. Just trying to understand this step.
okay so basically there is a rule in simplifying algebra; a(b -c) + d(b - c) = 0 then you can simplify i down to (b - c) (a + d) = 0 simply by pulling out the bracket with the common terms.
Okay thanks. I was thinking it was something like that, but wanted to be sure!

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