Answer
$x=0,4$ and $x=\frac{1}{3}$.
Work Step by Step
The given equation is
$\Rightarrow 6x^4+8x^2=26x^3$
Subtract $26x^3$ from each side.
$\Rightarrow 6x^4+8x^2-26x^3=26x^3-26x^3$
Simplify.
$\Rightarrow 6x^4+8x^2-26x^3=0$
$\Rightarrow 6x^4-26x^3+8x^2=0$
Factor out $2x^2$.
$\Rightarrow 2x^2(3x^2-13x+4)=0$
Rewrite $-13x$ as $-12x-x$.
$\Rightarrow 2x^2(3x^2-12x-x+4)=0$
Group the terms.
$\Rightarrow 2x^2[(3x^2-12x)+(-x+4)]=0$
Factor each group.
$\Rightarrow 2x^2[3x(x-4)-1(x-4)]=0$
Factor out $(x-4)$.
$\Rightarrow 2x^2(x-4)(3x-1)=0$
Use zero product property.
$\Rightarrow 2x^2=0$ or $x-4=0$ or $3x-1=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=4$ or $x=\frac{1}{3}$
The solutions are $x=0,4$ and $x=\frac{1}{3}$.
