12x^2+28x-15=0

Solution for 12x^2+28x-15=0 equation:

Simplifying
12x2 + 28x + -15 = 0

Reorder the terms:
-15 + 28x + 12x2 = 0

Solving
-15 + 28x + 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 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.333333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.333333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.333333333x + x2 = 0 + 1.25
2.333333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.333333333x + x2 = 1.25

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 1.25 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 1.25 + 1.361111112

Combine like terms: 1.25 + 1.361111112 = 2.611111112
1.361111112 + 2.333333333x + x2 = 2.611111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 2.611111112

Calculate the square root of the right side: 1.615893286

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.615893286 and -1.615893286.

Subproblem 1
x + 1.166666667 = 1.615893286

Simplifying
x + 1.166666667 = 1.615893286

Reorder the terms:
1.166666667 + x = 1.615893286

Solving
1.166666667 + x = 1.615893286

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.615893286 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.615893286 + -1.166666667
x = 1.615893286 + -1.166666667

Combine like terms: 1.615893286 + -1.166666667 = 0.449226619
x = 0.449226619

Simplifying
x = 0.449226619

Subproblem 2
x + 1.166666667 = -1.615893286

Simplifying
x + 1.166666667 = -1.615893286

Reorder the terms:
1.166666667 + x = -1.615893286

Solving
1.166666667 + x = -1.615893286

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.615893286 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.615893286 + -1.166666667
x = -1.615893286 + -1.166666667

Combine like terms: -1.615893286 + -1.166666667 = -2.782559953
x = -2.782559953

Simplifying
x = -2.782559953

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.449226619, -2.782559953}