Question

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

Answer 1

0,4,-4

Step-by-step 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} \\ (3c^2)/(3)=(48)/(3) \\ C^2=16 \\ \text{take the square root in both sides} \\ √(C^2)=√(16) \\ C=\pm4 \end{gathered}`

therefore, the answer is

`0,4,-4`