9a^2-30a+225=0

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Solution for 9a^2-30a+225=0 equation: 


Simplifying
9a2 + -30a + 225 = 0

Reorder the terms:
225 + -30a + 9a2 = 0

Solving
225 + -30a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(75 + -10a + 3a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(75 + -10a + 3a2)' equal to zero and attempt to solve:

Simplifying
75 + -10a + 3a2 = 0

Solving
75 + -10a + 3a2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
25 + -3.333333333a + a2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -3.333333333a + -25 + a2 = 0 + -25

Reorder the terms:
25 + -25 + -3.333333333a + a2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -3.333333333a + a2 = 0 + -25
-3.333333333a + a2 = 0 + -25

Combine like terms: 0 + -25 = -25
-3.333333333a + a2 = -25

The a term is -3.333333333a.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333a + 2.777777779 + a2 = -25 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333a + a2 = -25 + 2.777777779

Combine like terms: -25 + 2.777777779 = -22.222222221
2.777777779 + -3.333333333a + a2 = -22.222222221

Factor a perfect square on the left side:
(a + -1.666666667)(a + -1.666666667) = -22.222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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