Solve the equation 2c^4-6c^3=12c^2-36c The solutions are c=square , c=square and c=pm square

To solve the equation $2c^{4}-6c^{3}=12c^{2}-36c$, we first move all terms to one side of the equation to set it equal to zero:<br /><br />$2c^{4}-6c^{3}-12c^{2}+36c=0$<br /><br />Next, we factor out the greatest common factor, which is $2c$:<br /><br />$2c(c^{3}-3c^{2}-6c+18)=0$<br /><br />Now, we have a product of two factors equal to zero. We can set each factor equal to zero and solve for $c$:<br /><br />$2c=0$ or $c^{3}-3c^{2}-6c+18=0$<br /><br />Solving the first equation, we get $c=0$.<br /><br />To solve the second equation, we can use the quadratic formula or factor it further. In this case, we can factor it as:<br /><br />$(c-3)(c^{2}-6)=0$<br /><br />Setting each factor equal to zero, we get:<br /><br />$c-3=0$ or $c^{2}-6=0$<br /><br />Solving the first equation, we get $c=3$.<br /><br />Solving the second equation, we get $c=\pm \sqrt{6}$.<br /><br />Therefore, the solutions to the equation are $c=0$, $c=3$, and $c=\pm \sqrt{6}$.