__The equation in the problem is:__

$2x^{90}-4x^{89}=0$__Beginning__ Let's pay attention to the left side **The expression can be broken down into factors by taking out a common factor,** The **greatest** common factor for the numbers and letters in this case is $2x^{89}$and that is because the power of 89 is the __lowest power in the equation__ and therefore __included__ both in the term where the power is 90 and in the term where the power is 89, any power higher than that is __not included__ in the term where the power of 89 is the lowest, and therefore it is the term with the __highest power__ that can be taken out of all the terms in the expression as a common factor __for the letters__,

For the numbers, note that the number 4 is a multiple of the number 2, so the number 2 is the **greatest** common factor __for the numbers__ for the two terms in the expression,

**Continuing** if so and performing the factorization:

$2x^{90}-4x^{89}=0 \\
\downarrow\\
2x^{89}(x-2)=0$Let's continue and refer to the fact that on the left side of the equation that was obtained in the last step there is an algebraic expression and on the right side the number is 0, so, **since the only way to get the result 0 from a product is for at least**, __one of the factors in the product on the left side, must be equal to zero__,

Meaning:

$2x^{89}=0 \hspace{8pt}\text{/}:2\\
x^{89}=0 \hspace{8pt}\text{/}\sqrt[89]{\hspace{6pt}}\\
\boxed{x=0}$In the solution of the equation above, we first equated the two sides of the equation by moving the term with the unknown and then we took out a root of order 89 on both sides of the equation.

(In this case __taking out an odd-order root on the right side of the equation yields one possibility)__

__Or:__

$x-2=0 \\
\boxed{x=2}$

**In summary** if so the solution to the equation:

$2x^{90}-4x^{89}=0 \\
\downarrow\\
2x^{89}(x-2)=0 \\
\downarrow\\
2x^{89}=0 \rightarrow\boxed{ x=0}\\
x-2=0\rightarrow \boxed{x=2}\\
\downarrow\\
\boxed{x=0,2}$__And therefore the correct answer is answer a.__