10x^2+10x=12

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

Simplifying
10x2 + 10x = 12

Reorder the terms:
10x + 10x2 = 12

Solving
10x + 10x2 = 12

Solving for variable 'x'.

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

Combine like terms: 12 + -12 = 0
-12 + 10x + 10x2 = 0

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

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

Simplifying
-6 + 5x + 5x2 = 0

Solving
-6 + 5x + 5x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.2 + 0.25

Combine like terms: 1.2 + 0.25 = 1.45
1.25 + x2 = 1.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.45

Calculate the square root of the right side: 1.204159458

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.204159458 and -1.204159458.

Subproblem 1
x + 0.5 = 1.204159458

Simplifying
x + 0.5 = 1.204159458

Reorder the terms:
0.5 + x = 1.204159458

Solving
0.5 + x = 1.204159458

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.204159458 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.204159458 + -0.5
x = 1.204159458 + -0.5

Combine like terms: 1.204159458 + -0.5 = 0.704159458
x = 0.704159458

Simplifying
x = 0.704159458

Subproblem 2
x + 0.5 = -1.204159458

Simplifying
x + 0.5 = -1.204159458

Reorder the terms:
0.5 + x = -1.204159458

Solving
0.5 + x = -1.204159458

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.204159458 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.204159458 + -0.5
x = -1.204159458 + -0.5

Combine like terms: -1.204159458 + -0.5 = -1.704159458
x = -1.704159458

Simplifying
x = -1.704159458

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.704159458, -1.704159458}
Solution
x = {0.704159458, -1.704159458}