First we need to factor trinomial $ \color{blue}{ -16x^2+\dfrac{192}{5}x+\dfrac{24}{25} } $ and than we use factored form to solve an equation $ \color{blue}{ -16x^2+\dfrac{192}{5}x+\dfrac{24}{25} = 0} $.

Step 1: We can simplify equation by multiplying both sides by -25. After multiplying we have the following equation:

$$ \begin{aligned} -16x^2+\dfrac{192}{5}x+\dfrac{24}{25} &= 0 \,\,\, / \color{orangered}{\cdot \, -25 } \\[0.9 em ] 400x^2-960x-24 &=0 \end{aligned} $$

Step 2: Simplify equation by dividing all coefficients by 8

$$ \begin{aligned} 400x^2-960x-24 &= 0 \,\,\, / \color{orangered}{ : 8 } \\[0.9 em ] 50x^2-120x-3 &=0 \end{aligned} $$

Since the quadratic trinomial cannot be factored out we solved the problem using quadratic formula.

Quadratic Equation Solver