24x^2+8x+2=4-6x

Solution for 24x^2+8x+2=4-6x equation:

Simplifying
24x2 + 8x + 2 = 4 + -6x

Reorder the terms:
2 + 8x + 24x2 = 4 + -6x

Solving
2 + 8x + 24x2 = 4 + -6x

Solving for variable 'x'.

Reorder the terms:
2 + -4 + 8x + 6x + 24x2 = 4 + -6x + -4 + 6x

Combine like terms: 2 + -4 = -2
-2 + 8x + 6x + 24x2 = 4 + -6x + -4 + 6x

Combine like terms: 8x + 6x = 14x
-2 + 14x + 24x2 = 4 + -6x + -4 + 6x

Reorder the terms:
-2 + 14x + 24x2 = 4 + -4 + -6x + 6x

Combine like terms: 4 + -4 = 0
-2 + 14x + 24x2 = 0 + -6x + 6x
-2 + 14x + 24x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-2 + 14x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 7x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 7x + 12x2)' equal to zero and attempt to solve:

Simplifying
-1 + 7x + 12x2 = 0

Solving
-1 + 7x + 12x2 = 0

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

Divide each side by '12'.
-0.08333333333 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.5833333333x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.5833333333x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.5833333333x + x2 = 0 + 0.08333333333
0.5833333333x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
0.5833333333x + x2 = 0.08333333333

The x term is 0.5833333333x.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333x + 0.08506944446 + x2 = 0.08333333333 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 0.08333333333 + 0.08506944446

Combine like terms: 0.08333333333 + 0.08506944446 = 0.16840277779
0.08506944446 + 0.5833333333x + x2 = 0.16840277779

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 0.16840277779

Calculate the square root of the right side: 0.410369075

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 0.410369075 and -0.410369075.

Subproblem 1
x + 0.2916666667 = 0.410369075

Simplifying
x + 0.2916666667 = 0.410369075

Reorder the terms:
0.2916666667 + x = 0.410369075

Solving
0.2916666667 + x = 0.410369075

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = 0.410369075 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = 0.410369075 + -0.2916666667
x = 0.410369075 + -0.2916666667

Combine like terms: 0.410369075 + -0.2916666667 = 0.1187024083
x = 0.1187024083

Simplifying
x = 0.1187024083

Subproblem 2
x + 0.2916666667 = -0.410369075

Simplifying
x + 0.2916666667 = -0.410369075

Reorder the terms:
0.2916666667 + x = -0.410369075

Solving
0.2916666667 + x = -0.410369075

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = -0.410369075 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = -0.410369075 + -0.2916666667
x = -0.410369075 + -0.2916666667

Combine like terms: -0.410369075 + -0.2916666667 = -0.7020357417
x = -0.7020357417

Simplifying
x = -0.7020357417

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1187024083, -0.7020357417}
Solution
x = {0.1187024083, -0.7020357417}