6x^2+10x=4-10x-6x^2

Solution for 6x^2+10x=4-10x-6x^2 equation:

Simplifying
6x2 + 10x = 4 + -10x + -6x2

Reorder the terms:
10x + 6x2 = 4 + -10x + -6x2

Solving
10x + 6x2 = 4 + -10x + -6x2

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + 10x + 6x2 + 6x2 = 4 + -10x + -6x2 + -4 + 10x + 6x2

Combine like terms: 10x + 10x = 20x
-4 + 20x + 6x2 + 6x2 = 4 + -10x + -6x2 + -4 + 10x + 6x2

Combine like terms: 6x2 + 6x2 = 12x2
-4 + 20x + 12x2 = 4 + -10x + -6x2 + -4 + 10x + 6x2

Reorder the terms:
-4 + 20x + 12x2 = 4 + -4 + -10x + 10x + -6x2 + 6x2

Combine like terms: 4 + -4 = 0
-4 + 20x + 12x2 = 0 + -10x + 10x + -6x2 + 6x2
-4 + 20x + 12x2 = -10x + 10x + -6x2 + 6x2

Combine like terms: -10x + 10x = 0
-4 + 20x + 12x2 = 0 + -6x2 + 6x2
-4 + 20x + 12x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + 20x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x + 3x2 = 0

Solving
-1 + 5x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 1.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 1.666666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + 0.3333333333
1.666666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
1.666666667x + x2 = 0.3333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.3333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.3333333333 + 0.6944444447

Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778
0.6944444447 + 1.666666667x + x2 = 1.027777778

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.027777778

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.013793755 and -1.013793755.

Subproblem 1
x + 0.8333333335 = 1.013793755

Simplifying
x + 0.8333333335 = 1.013793755

Reorder the terms:
0.8333333335 + x = 1.013793755

Solving
0.8333333335 + x = 1.013793755

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.013793755 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.013793755 + -0.8333333335
x = 1.013793755 + -0.8333333335

Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215
x = 0.1804604215

Simplifying
x = 0.1804604215

Subproblem 2
x + 0.8333333335 = -1.013793755

Simplifying
x + 0.8333333335 = -1.013793755

Reorder the terms:
0.8333333335 + x = -1.013793755

Solving
0.8333333335 + x = -1.013793755

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.013793755 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.013793755 + -0.8333333335
x = -1.013793755 + -0.8333333335

Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885
x = -1.8471270885

Simplifying
x = -1.8471270885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1804604215, -1.8471270885}
Solution
x = {0.1804604215, -1.8471270885}