Answer
The solutions are $x=\frac{4}{5}$ and $x=\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow -10x^2+13x=4$
Subtract $4$ from each side.
$\Rightarrow -10x^2+13x-4=0$
The equation is easily factorable. So, solve by factoring.
$\Rightarrow -10x^2+13x-4=0$
Rewrite $13x$ as $8x+5x$.
$\Rightarrow -10x^2+8x+5x-4=0$
Group the terms.
$\Rightarrow (-10x^2+8x)+(5x-4)=0$
Factor each group.
$\Rightarrow -2x(5x-4)+1(5x-4)=0$
Factor out $(5x-4)$.
$\Rightarrow (5x-4)(-2x+1)=0$
Use zero-product property.
$\Rightarrow 5x-4=0$ or $-2x+1=0$
Solve for $x$.
$\Rightarrow x=\frac{4}{5}$ or $x=\frac{1}{2}$
Hence, the solutions are $x=\frac{4}{5}$ and $x=\frac{1}{2}$.
