Certainly, let's solve the given equation step-by-step.
We are given the equation:
[tex]\[
(x + 4) \cdot (5x + 2)^{0} = 0
\][/tex]
1. First, observe that anything raised to the power 0 is 1, as long as it isn't zero itself. Therefore, [tex]\( (5x + 2)^{0} = 1 \)[/tex].
2. The equation simplifies to:
[tex]\[
(x + 4) \cdot 1 = 0
\][/tex]
3. This further simplifies to:
[tex]\[
x + 4 = 0
\][/tex]
4. To isolate [tex]\( x \)[/tex], we subtract 4 from both sides of the equation:
[tex]\[
x = -4
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = -4
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies the given equation is [tex]\( -4 \)[/tex].
