Question

solve the equation $2c^{4}-6c^{3}=12c^{2}-36c$. the solutions are $c = \square$, $c = \square$, and $c = \pm \square$.

Explanation:

Step1: Move all terms to left side

$2c^4 - 6c^3 - 12c^2 + 36c = 0$

Step2: Factor by grouping

$2c^3(c - 3) - 12c(c - 3) = 0$

Step3: Factor out common binomial

$(2c^3 - 12c)(c - 3) = 0$

Step4: Factor out GCF from first term

$2c(c^2 - 6)(c - 3) = 0$

Step5: Set each factor to 0

$2c=0$, $c-3=0$, $c^2-6=0$

Step6: Solve each equation

$c=0$; $c=3$; $c=\pm\sqrt{6}$

Answer:

$c = 0$, $c = 3$, and $c = \pm \sqrt{6}$