To find the value of the constant [tex]\(c\)[/tex] in the given equation
[tex]\[
-4\left(2 x^2 - 3\right) = -8 x^2 + c,
\][/tex]
we need to simplify and compare both sides of the equation step-by-step.
1. Distribute the [tex]\(-4\)[/tex] on the left side of the equation:
[tex]\[
-4 \left(2 x^2 - 3\right) = -4 \cdot 2 x^2 -4 \cdot (-3).
\][/tex]
Simplifying the multiplication, we get:
[tex]\[
-8 x^2 + 12.
\][/tex]
2. Rewrite the given equation with the simplified left side:
[tex]\[
-8 x^2 + 12 = -8 x^2 + c.
\][/tex]
3. Compare the simplified left side expression with the right side of the equation:
We can see that the terms involving [tex]\(x^2\)[/tex] are identical on both sides. Therefore, what remains is to equate the constant terms on each side. That is:
[tex]\[
12 = c.
\][/tex]
Therefore, the value of [tex]\(c\)[/tex] is:
[tex]\[
\boxed{12}
\][/tex]
