10x^2-24x+12=0

Solution for 10x^2-24x+12=0 equation:

Simplifying
10x2 + -24x + 12 = 0

Reorder the terms:
12 + -24x + 10x2 = 0

Solving
12 + -24x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -12x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -12x + 5x2)' equal to zero and attempt to solve:

Simplifying
6 + -12x + 5x2 = 0

Solving
6 + -12x + 5x2 = 0

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

Divide each side by '5'.
1.2 + -2.4x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -2.4x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -2.4x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -2.4x + x2 = 0 + -1.2
-2.4x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-2.4x + x2 = -1.2

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = -1.2 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = -1.2 + 1.44

Combine like terms: -1.2 + 1.44 = 0.24
1.44 + -2.4x + x2 = 0.24

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(x + -1.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
x + -1.2 = 0.489897949

Simplifying
x + -1.2 = 0.489897949

Reorder the terms:
-1.2 + x = 0.489897949

Solving
-1.2 + x = 0.489897949

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 0.489897949 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 0.489897949 + 1.2
x = 0.489897949 + 1.2

Combine like terms: 0.489897949 + 1.2 = 1.689897949
x = 1.689897949

Simplifying
x = 1.689897949

Subproblem 2
x + -1.2 = -0.489897949

Simplifying
x + -1.2 = -0.489897949

Reorder the terms:
-1.2 + x = -0.489897949

Solving
-1.2 + x = -0.489897949

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -0.489897949 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -0.489897949 + 1.2
x = -0.489897949 + 1.2

Combine like terms: -0.489897949 + 1.2 = 0.710102051
x = 0.710102051

Simplifying
x = 0.710102051

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.689897949, 0.710102051}
Solution
x = {1.689897949, 0.710102051}