To determine which of the provided values for [tex]\( x \)[/tex] is a solution to the equation [tex]\((x - 3)(x + 9) = -27\)[/tex], we can substitute each value into the equation and check if it satisfies the equation.
1. Testing [tex]\( x = -9 \)[/tex]:
[tex]\[
(x - 3)(x + 9) = (-9 - 3)(-9 + 9) = (-12)(0) = 0
\][/tex]
This does not satisfy [tex]\((x - 3)(x + 9) = -27\)[/tex].
2. Testing [tex]\( x = -3 \)[/tex]:
[tex]\[
(x - 3)(x + 9) = (-3 - 3)(-3 + 9) = (-6)(6) = -36
\][/tex]
This does not satisfy [tex]\((x - 3)(x + 9) = -27\)[/tex].
3. Testing [tex]\( x = 0 \)[/tex]:
[tex]\[
(x - 3)(x + 9) = (0 - 3)(0 + 9) = (-3)(9) = -27
\][/tex]
This satisfies [tex]\((x - 3)(x + 9) = -27\)[/tex].
4. Testing [tex]\( x = 6 \)[/tex]:
[tex]\[
(x - 3)(x + 9) = (6 - 3)(6 + 9) = (3)(15) = 45
\][/tex]
This does not satisfy [tex]\((x - 3)(x + 9) = -27\)[/tex].
Thus, the only value of [tex]\( x \)[/tex] that satisfies the equation [tex]\((x - 3)(x + 9) = -27\)[/tex] is [tex]\( x = 0 \)[/tex].
