24x*14+8=76x*12x-6

Solution for 24x*14+8=76x*12x-6 equation:

Simplifying
24x * 14 + 8 = 76x * 12x + -6

Reorder the terms for easier multiplication:
24 * 14x + 8 = 76x * 12x + -6

Multiply 24 * 14
336x + 8 = 76x * 12x + -6

Reorder the terms:
8 + 336x = 76x * 12x + -6

Reorder the terms for easier multiplication:
8 + 336x = 76 * 12x * x + -6

Multiply 76 * 12
8 + 336x = 912x * x + -6

Multiply x * x
8 + 336x = 912x2 + -6

Reorder the terms:
8 + 336x = -6 + 912x2

Solving
8 + 336x = -6 + 912x2

Solving for variable 'x'.

Reorder the terms:
8 + 6 + 336x + -912x2 = -6 + 912x2 + 6 + -912x2

Combine like terms: 8 + 6 = 14
14 + 336x + -912x2 = -6 + 912x2 + 6 + -912x2

Reorder the terms:
14 + 336x + -912x2 = -6 + 6 + 912x2 + -912x2

Combine like terms: -6 + 6 = 0
14 + 336x + -912x2 = 0 + 912x2 + -912x2
14 + 336x + -912x2 = 912x2 + -912x2

Combine like terms: 912x2 + -912x2 = 0
14 + 336x + -912x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 168x + -456x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 168x + -456x2)' equal to zero and attempt to solve:

Simplifying
7 + 168x + -456x2 = 0

Solving
7 + 168x + -456x2 = 0

Begin completing the square.  Divide all terms by
-456 the coefficient of the squared term: 

Divide each side by '-456'.
-0.01535087719 + -0.3684210526x + x2 = 0

Move the constant term to the right:

Add '0.01535087719' to each side of the equation.
-0.01535087719 + -0.3684210526x + 0.01535087719 + x2 = 0 + 0.01535087719

Reorder the terms:
-0.01535087719 + 0.01535087719 + -0.3684210526x + x2 = 0 + 0.01535087719

Combine like terms: -0.01535087719 + 0.01535087719 = 0.00000000000
0.00000000000 + -0.3684210526x + x2 = 0 + 0.01535087719
-0.3684210526x + x2 = 0 + 0.01535087719

Combine like terms: 0 + 0.01535087719 = 0.01535087719
-0.3684210526x + x2 = 0.01535087719

The x term is -0.3684210526x.  Take half its coefficient (-0.1842105263).
Square it (0.03393351800) and add it to both sides.

Add '0.03393351800' to each side of the equation.
-0.3684210526x + 0.03393351800 + x2 = 0.01535087719 + 0.03393351800

Reorder the terms:
0.03393351800 + -0.3684210526x + x2 = 0.01535087719 + 0.03393351800

Combine like terms: 0.01535087719 + 0.03393351800 = 0.04928439519
0.03393351800 + -0.3684210526x + x2 = 0.04928439519

Factor a perfect square on the left side:
(x + -0.1842105263)(x + -0.1842105263) = 0.04928439519

Calculate the square root of the right side: 0.22200089

Break this problem into two subproblems by setting 
(x + -0.1842105263) equal to 0.22200089 and -0.22200089.

Subproblem 1
x + -0.1842105263 = 0.22200089

Simplifying
x + -0.1842105263 = 0.22200089

Reorder the terms:
-0.1842105263 + x = 0.22200089

Solving
-0.1842105263 + x = 0.22200089

Solving for variable 'x'.

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

Add '0.1842105263' to each side of the equation.
-0.1842105263 + 0.1842105263 + x = 0.22200089 + 0.1842105263

Combine like terms: -0.1842105263 + 0.1842105263 = 0.0000000000
0.0000000000 + x = 0.22200089 + 0.1842105263
x = 0.22200089 + 0.1842105263

Combine like terms: 0.22200089 + 0.1842105263 = 0.4062114163
x = 0.4062114163

Simplifying
x = 0.4062114163

Subproblem 2
x + -0.1842105263 = -0.22200089

Simplifying
x + -0.1842105263 = -0.22200089

Reorder the terms:
-0.1842105263 + x = -0.22200089

Solving
-0.1842105263 + x = -0.22200089

Solving for variable 'x'.

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

Add '0.1842105263' to each side of the equation.
-0.1842105263 + 0.1842105263 + x = -0.22200089 + 0.1842105263

Combine like terms: -0.1842105263 + 0.1842105263 = 0.0000000000
0.0000000000 + x = -0.22200089 + 0.1842105263
x = -0.22200089 + 0.1842105263

Combine like terms: -0.22200089 + 0.1842105263 = -0.0377903637
x = -0.0377903637

Simplifying
x = -0.0377903637

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4062114163, -0.0377903637}
Solution
x = {0.4062114163, -0.0377903637}