9x^2-54x+105=0

Solution for 9x^2-54x+105=0 equation:

Simplifying
9x2 + -54x + 105 = 0

Reorder the terms:
105 + -54x + 9x2 = 0

Solving
105 + -54x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + -18x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(35 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
35 + -18x + 3x2 = 0

Solving
35 + -18x + 3x2 = 0

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

Divide each side by '3'.
11.66666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-11.66666667' to each side of the equation.
11.66666667 + -6x + -11.66666667 + x2 = 0 + -11.66666667

Reorder the terms:
11.66666667 + -11.66666667 + -6x + x2 = 0 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + -6x + x2 = 0 + -11.66666667
-6x + x2 = 0 + -11.66666667

Combine like terms: 0 + -11.66666667 = -11.66666667
-6x + x2 = -11.66666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -11.66666667 + 9

Reorder the terms:
9 + -6x + x2 = -11.66666667 + 9

Combine like terms: -11.66666667 + 9 = -2.66666667
9 + -6x + x2 = -2.66666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = -2.66666667

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.