What are the solutions to the equation 3(x – 4)(x + 5) = 0?

x = –4 or x = 5
x = 3, x = 4, or x = –5
x = 3, x = –4, or x = 5
x = 4 or x = –5

The correct answer is:  [D]:  " x = 4 or x = -5 " .

Note:  Divide each side of the equation by "3" ;

[3(x – 4)(x + 5)] / 3 = 0 / 3 ;

to get:

(x – 4)(x + 5) = 0 ;

So, the equation holds true if either:

(x – 4) = 0 ;  or:

(x + 5) = 0 ;

Since:  "(x – 4)" and  "(x + 5)" are the products; one of these products must equal "zero" for the equation to equal zero.

So, for:   x – 4 = 0 ;  add "4" to each side of the equation;

               x – 4 + 4 = 0 + 4 ;

to get:   x = 4 ;

For:  x + 5 = 0 ; subtract "5" from each side of the equation:

               x + 5 – 5 = 0 – 5 ;

to get:  x = -5 ;

So, we have:  x = 4, -5  ;  which is Answer choice:  [D]:  " x = 4 or x = -5 " .

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