12x^2-32x+15=0

Solution for 12x^2-32x+15=0 equation:

Simplifying
12x2 + -32x + 15 = 0

Reorder the terms:
15 + -32x + 12x2 = 0

Solving
15 + -32x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
1.25 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.666666667x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.666666667x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.666666667x + x2 = 0 + -1.25
-2.666666667x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.666666667x + x2 = -1.25

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 = -1.25 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -1.25 + 1.777777780

Combine like terms: -1.25 + 1.777777780 = 0.52777778
1.777777780 + -2.666666667x + x2 = 0.52777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 0.52777778

Calculate the square root of the right side: 0.726483159

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 0.726483159 and -0.726483159.

Subproblem 1
x + -1.333333334 = 0.726483159

Simplifying
x + -1.333333334 = 0.726483159

Reorder the terms:
-1.333333334 + x = 0.726483159

Solving
-1.333333334 + x = 0.726483159

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 0.726483159 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 0.726483159 + 1.333333334
x = 0.726483159 + 1.333333334

Combine like terms: 0.726483159 + 1.333333334 = 2.059816493
x = 2.059816493

Simplifying
x = 2.059816493

Subproblem 2
x + -1.333333334 = -0.726483159

Simplifying
x + -1.333333334 = -0.726483159

Reorder the terms:
-1.333333334 + x = -0.726483159

Solving
-1.333333334 + x = -0.726483159

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -0.726483159 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -0.726483159 + 1.333333334
x = -0.726483159 + 1.333333334

Combine like terms: -0.726483159 + 1.333333334 = 0.606850175
x = 0.606850175

Simplifying
x = 0.606850175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.059816493, 0.606850175}