Sure, let's solve this quadratic equation using the factorization method.
First, we need to factor the given quadratic equation, which is 10x² - 25x + 15 = 0
The factored form of this equation is written as 5*(x - 1)*(2x - 3) = 0.
Here, the constituents of the equation (x-1) and (2x - 3) are multiplied together to equal to zero.
When a product is zero, one or both of the factors must be zero.
Using this property, we can now go ahead and solve for 'x' from these two factors.
Firstly, set each factor equal to zero and solve for 'x':
1) x - 1 = 0 => x = 1
2) 2x - 3 = 0 => 2x = 3 => x = 3/2
These are the two solutions for 'x' which make the original equation 10x² - 25x + 15 = 0 equal to zero. Hence, the roots of the equation are 1 and 3/2.