How do you solve $x (x + 3) (x - 4) = 0$ $x(x+3)(x-4)=0$ ?

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Answer 1 · 2016-12-12T17:58:45

See explanation.

In such examples you can use the following property of real numbers (expressions):

A product of expressions is zero if and only if any of these expressions is zero.

If you use the property in this example you get:

$x (x + 3) (x - 4) = 0 \Leftrightarrow x = 0 \lor x + 3 = 0 \lor x - 4 = 0$ $x(x+3)(x-4)=0 iff x=0 vv x+3=0 vv x-4=0$

In this way one equation of 3rd degree is changed to 3 linear equations:

After solving them you get the final answer:

$x = 0 \lor x = - 3 \lor x = 4$ $x=0 vv x=-3 vv x=4$