$$(2x^2-3x+1)(x^2-1) = 0$$

$ \color{blue}{ 2x^{4}-3x^{3}-x^{2}+3x-1 } $ is a polynomial of degree 4. To find zeros for polynomials of degree 3 or higher we use Rational Root Test.

The Rational Root Theorem tells you that if the polynomial has a rational zero then it must be a fraction $ \dfrac{p}{q} $, where p is a factor of the trailing constant and q is a factor of the leading coefficient.

The factors of the leading coefficient ( 2 ) are 1 2 .The factor of the constant term ( -1 ) is 1 . Then the Rational Roots Tests yields the following possible solutions:

Substitute the POSSIBLE roots one by one into the polynomial to find the actual roots. Start first with the whole numbers.

If we plug these values into the polynomial $ P(x) $, we obtain $ P(1) = 0 $.

To find remaining zeros we use Factor Theorem. This theorem states that if $\frac{p}{q}$ is root of the polynomial then this polynomial can be divided with $ \color{blue}{q x - p} $. In this example:

Divide $ P(x) $ with $ \color{blue}{x - 1} $

Polynomial $ 2x^{3}-x^{2}-2x+1 $ can be used to find the remaining roots.

Use the same procedure to find roots of $ 2x^{3}-x^{2}-2x+1 $

When you get second degree polynomial use step-by-step quadratic equation solver to find two remaining roots.