To solve this problem, we would first expand the right hand side of the equation making the equation as follows:
3x² + bx + 10 = ax² + 6ax + 9a + c
Following this, we need to make sure we match coefficients on both sides of the equation for each power of x.
Matching the coefficient of x²:
On the left hand side, the coefficient of x² is 3
On the right hand side, the coefficient of x² is a
So, we have:
3 = a
So, a = 3.
Next, we match the coefficients of x:
On the left hand side, we have b
On the right hand side, we have 6a = 6*3 = 18
So, we have:
b = 18
Lastly, we match the constant terms:
On the left hand side, we have 10
On the right hand side, we have 9a + c = 9*3 + c = 27 + c
So we have:
10 = 27+c
Rearranging, we'll get:
c = 10 - 27 = -17
So, the solution for the symbols a, b, and c are 3, 18, and -17 respectively.