10x^2+28x+12=0

Solution for 10x^2+28x+12=0 equation:

Simplifying
10x2 + 28x + 12 = 0

Reorder the terms:
12 + 28x + 10x2 = 0

Solving
12 + 28x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 14x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 14x + 5x2)' equal to zero and attempt to solve:

Simplifying
6 + 14x + 5x2 = 0

Solving
6 + 14x + 5x2 = 0

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

Divide each side by '5'.
1.2 + 2.8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.8x + x2 = 0 + -1.2
2.8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.8x + x2 = -1.2

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = -1.2 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = -1.2 + 1.96

Combine like terms: -1.2 + 1.96 = 0.76
1.96 + 2.8x + x2 = 0.76

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(x + 1.4) equal to 0.871779789 and -0.871779789.

Subproblem 1
x + 1.4 = 0.871779789

Simplifying
x + 1.4 = 0.871779789

Reorder the terms:
1.4 + x = 0.871779789

Solving
1.4 + x = 0.871779789

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = 0.871779789 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = 0.871779789 + -1.4
x = 0.871779789 + -1.4

Combine like terms: 0.871779789 + -1.4 = -0.528220211
x = -0.528220211

Simplifying
x = -0.528220211

Subproblem 2
x + 1.4 = -0.871779789

Simplifying
x + 1.4 = -0.871779789

Reorder the terms:
1.4 + x = -0.871779789

Solving
1.4 + x = -0.871779789

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = -0.871779789 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = -0.871779789 + -1.4
x = -0.871779789 + -1.4

Combine like terms: -0.871779789 + -1.4 = -2.271779789
x = -2.271779789

Simplifying
x = -2.271779789

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.528220211, -2.271779789}
Solution
x = {-0.528220211, -2.271779789}