Question 119765
To begin you need to make one side equal to zero to get the total equation so you can solve for x.

3x^2-2x = 15x-10

subtract 15x and -10 from both sides

3x^2 - 2x - 15x - (-10)= 15x - 10 - 15x - (-10)

Simplify

3x^2 - 17x +10 = 0

Now you will break down this equation into two simpler equations. To do this you must determine which factors are needed.  For example we know that 3's factors are only 3 and 1, however for 10 the factors are either 10 and 1 or 5 and 2.  To determine which of these two to use you must look to the middle number, which is 17x.  The factors that would make - 17x would be - 5 and -2 where 5 is going to be the factor that is multipled by 3x and 2 is the factor being multiplied by 1x.

(3x - 2)(x - 5) = 0

3x - 2 = 0 and x - 5 = 0

start with 3x - 2 = 0

add 2 to both sides

3x - 2 + 2 = 0 + 2

3x = 2

divide both sides by 3

3x/3 = 2/3

x = 2/3

now for the second part

x - 5 = 0

add 5 to both sides

x - 5 + 5 = 0 + 5

x = 5

So your solution will be x = 2/3, 5

To check your solution plug one of the answers for x into your orginal equation and solve.