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Solve the two equations from the factored form [tex]6(x+7)(x-4)=0[/tex].

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Sagot :

GinnyAnswer
To solve the given equation [tex]\( 6(x + 7)(x - 4) = 0 \)[/tex], you can follow these steps:

1. Begin by noting that the product of the factors is equal to zero. According to the zero-product property, if a product of several factors equals zero, at least one of the factors must be zero.

2. Set each factor equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ x + 7 = 0 \implies x = -7 \][/tex]
[tex]\[ x - 4 = 0 \implies x = 4 \][/tex]

3. Thus, the solutions to the equation [tex]\( 6(x + 7)(x - 4) = 0 \)[/tex] are:
[tex]\[ x = -7 \text{ or } x = 4 \][/tex]

Enter the solutions in the boxes:
[tex]\[ x = \boxed{-7} \text{ or } x = \boxed{4} \][/tex]
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