12x^2-20x+24=0

Solution for 12x^2-20x+24=0 equation:

Simplifying
12x2 + -20x + 24 = 0

Reorder the terms:
24 + -20x + 12x2 = 0

Solving
24 + -20x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -5x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -5x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + -5x + 3x2 = 0

Solving
6 + -5x + 3x2 = 0

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

Divide each side by '3'.
2 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.666666667x + x2 = 0 + -2
-1.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.666666667x + x2 = -2

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -2 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -2 + 0.6944444447

Combine like terms: -2 + 0.6944444447 = -1.3055555553
0.6944444447 + -1.666666667x + x2 = -1.3055555553

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -1.3055555553

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.