-6x(4x+1)+4=

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Solution for -6x(4x+1)+4= equation: 


Simplifying
-6x(4x + 1) + 4 = 0

Reorder the terms:
-6x(1 + 4x) + 4 = 0
(1 * -6x + 4x * -6x) + 4 = 0
(-6x + -24x2) + 4 = 0

Reorder the terms:
4 + -6x + -24x2 = 0

Solving
4 + -6x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + -12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -3x + -12x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + -12x2 = 0

Solving
2 + -3x + -12x2 = 0

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

Divide each side by '-12'.
-0.1666666667 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.25x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.25x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.25x + x2 = 0 + 0.1666666667
0.25x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.25x + x2 = 0.1666666667

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.1666666667 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.1666666667 + 0.015625

Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667
0.015625 + 0.25x + x2 = 0.1822916667

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.1822916667

Calculate the square root of the right side: 0.426956282

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.426956282 and -0.426956282.


Subproblem 1
x + 0.125 = 0.426956282

Simplifying
x + 0.125 = 0.426956282

Reorder the terms:
0.125 + x = 0.426956282

Solving
0.125 + x = 0.426956282

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.426956282 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.426956282 + -0.125
x = 0.426956282 + -0.125

Combine like terms: 0.426956282 + -0.125 = 0.301956282
x = 0.301956282

Simplifying
x = 0.301956282


Subproblem 2
x + 0.125 = -0.426956282

Simplifying
x + 0.125 = -0.426956282

Reorder the terms:
0.125 + x = -0.426956282

Solving
0.125 + x = -0.426956282

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.426956282 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.426956282 + -0.125
x = -0.426956282 + -0.125

Combine like terms: -0.426956282 + -0.125 = -0.551956282
x = -0.551956282

Simplifying
x = -0.551956282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.301956282, -0.551956282}
Solution
x = {0.301956282, -0.551956282}

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