factor \( 6 x^{4}+8 x^{2}=26 x^{3} \)

To factor the equation \( 6x^{4} + 8x^{2} = 26x^{3} \), we first rearrange it into standard form: \[ 6x^{4} - 26x^{3} + 8x^{2} = 0. \] Next, we can factor out the common term, which is \( 2x^{2} \): \[ 2x^{2}(3x^{2} - 13x + 4) = 0. \] Now, we need to factor the quadratic \( 3x^{2} - 13x + 4 \). This factors into \( (3x - 1)(x - 4) = 0 \). So, the complete factored form is: \[ 2x^{2}(3x - 1)(x - 4) = 0. \] Setting each factor to zero gives the solutions \( x = 0 \), \( x = \frac{1}{3} \), and \( x = 4 \).