15x^2-40x+65=0

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Solution for 15x^2-40x+65=0 equation: 


Simplifying
15x2 + -40x + 65 = 0

Reorder the terms:
65 + -40x + 15x2 = 0

Solving
65 + -40x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + -8x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
13 + -8x + 3x2 = 0

Solving
13 + -8x + 3x2 = 0

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

Divide each side by '3'.
4.333333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + -2.666666667x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + -2.666666667x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -4.333333333
-2.666666667x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
-2.666666667x + x2 = -4.333333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -4.333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -4.333333333 + 1.777777780

Combine like terms: -4.333333333 + 1.777777780 = -2.555555553
1.777777780 + -2.666666667x + x2 = -2.555555553

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = -2.555555553

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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