10x^2-20x-12=0

Solution for 10x^2-20x-12=0 equation:

Simplifying
10x2 + -20x + -12 = 0

Reorder the terms:
-12 + -20x + 10x2 = 0

Solving
-12 + -20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -10x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -10x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + -10x + 5x2 = 0

Solving
-6 + -10x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -2x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2x + x2 = 0 + 1.2
-2x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2x + x2 = 1.2

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.2 + 1

Reorder the terms:
1 + -2x + x2 = 1.2 + 1

Combine like terms: 1.2 + 1 = 2.2
1 + -2x + x2 = 2.2

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.2

Calculate the square root of the right side: 1.483239697

Break this problem into two subproblems by setting 
(x + -1) equal to 1.483239697 and -1.483239697.

Subproblem 1
x + -1 = 1.483239697

Simplifying
x + -1 = 1.483239697

Reorder the terms:
-1 + x = 1.483239697

Solving
-1 + x = 1.483239697

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.483239697 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.483239697 + 1
x = 1.483239697 + 1

Combine like terms: 1.483239697 + 1 = 2.483239697
x = 2.483239697

Simplifying
x = 2.483239697

Subproblem 2
x + -1 = -1.483239697

Simplifying
x + -1 = -1.483239697

Reorder the terms:
-1 + x = -1.483239697

Solving
-1 + x = -1.483239697

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.483239697 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.483239697 + 1
x = -1.483239697 + 1

Combine like terms: -1.483239697 + 1 = -0.483239697
x = -0.483239697

Simplifying
x = -0.483239697

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.483239697, -0.483239697}
Solution
x = {2.483239697, -0.483239697}