2+7x(6x+4)=

Solution for 2+7x(6x+4)= equation:

Simplifying
2 + 7x(6x + 4) = 0

Reorder the terms:
2 + 7x(4 + 6x) = 0
2 + (4 * 7x + 6x * 7x) = 0
2 + (28x + 42x2) = 0

Solving
2 + 28x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 14x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 14x + 21x2)' equal to zero and attempt to solve:

Simplifying
1 + 14x + 21x2 = 0

Solving
1 + 14x + 21x2 = 0

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

Divide each side by '21'.
0.04761904762 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.04761904762' to each side of the equation.
0.04761904762 + 0.6666666667x + -0.04761904762 + x2 = 0 + -0.04761904762

Reorder the terms:
0.04761904762 + -0.04761904762 + 0.6666666667x + x2 = 0 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + 0.6666666667x + x2 = 0 + -0.04761904762
0.6666666667x + x2 = 0 + -0.04761904762

Combine like terms: 0 + -0.04761904762 = -0.04761904762
0.6666666667x + x2 = -0.04761904762

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -0.04761904762 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -0.04761904762 + 0.1111111112

Combine like terms: -0.04761904762 + 0.1111111112 = 0.06349206358
0.1111111112 + 0.6666666667x + x2 = 0.06349206358

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.06349206358

Calculate the square root of the right side: 0.251976316

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.251976316 and -0.251976316.

Subproblem 1
x + 0.3333333334 = 0.251976316

Simplifying
x + 0.3333333334 = 0.251976316

Reorder the terms:
0.3333333334 + x = 0.251976316

Solving
0.3333333334 + x = 0.251976316

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.251976316 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.251976316 + -0.3333333334
x = 0.251976316 + -0.3333333334

Combine like terms: 0.251976316 + -0.3333333334 = -0.0813570174
x = -0.0813570174

Simplifying
x = -0.0813570174

Subproblem 2
x + 0.3333333334 = -0.251976316

Simplifying
x + 0.3333333334 = -0.251976316

Reorder the terms:
0.3333333334 + x = -0.251976316

Solving
0.3333333334 + x = -0.251976316

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.251976316 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.251976316 + -0.3333333334
x = -0.251976316 + -0.3333333334

Combine like terms: -0.251976316 + -0.3333333334 = -0.5853096494
x = -0.5853096494

Simplifying
x = -0.5853096494

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0813570174, -0.5853096494}
Solution
x = {-0.0813570174, -0.5853096494}