Question

solve the equation give exact awnserd only enter your awnser as a comma separated list.

Answer 1

0,4,-4

Explanation

$3c^3-48c=0$

Step 1

we can see both terms in the equation have c, so C is a common factor.

Let's factorize it

hence

$\begin{gathered} 3c^3-48c=0 \\ c(3c^2-48)=0 \\ \text{therefore, we have 2 factors} \\ (c)((3c^2-48)=0 \end{gathered}$

Step 2

now, when the product of 2 numbers equal zero:

$(c)(3c^2-48)=0$

is because

1) one of the two numbers is zero

2) both numbers are zero

so

$\begin{gathered} C\text{ =0} \\ is\text{ a solution } \end{gathered}$

Step 3

finally, we need to check when the second factor is zero

so

$\begin{gathered} 3c^2-48=0 \\ \text{add 48 in both sides} \\ 3c^2-48+48=0+48 \\ 3c^2=48 \\ \text{divide both sides by 3} \\ \frac{3c^2}{3}=\frac{48}{3} \\ C^2=16 \\ \text{take the square root in both sides} \\ \sqrt{C^2}=\sqrt{16} \\ C=\pm4 \end{gathered}$

therefore, the answer is

$0,4,-4$