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]
