3x(4x-1)-2=19

Solution for 3x(4x-1)-2=19 equation:

Simplifying
3x(4x + -1) + -2 = 19

Reorder the terms:
3x(-1 + 4x) + -2 = 19
(-1 * 3x + 4x * 3x) + -2 = 19
(-3x + 12x2) + -2 = 19

Reorder the terms:
-2 + -3x + 12x2 = 19

Solving
-2 + -3x + 12x2 = 19

Solving for variable 'x'.

Reorder the terms:
-2 + -19 + -3x + 12x2 = 19 + -19

Combine like terms: -2 + -19 = -21
-21 + -3x + 12x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-21 + -3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -1x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-7 + -1x + 4x2 = 0

Solving
-7 + -1x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.25x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.25x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.25x + x2 = 0 + 1.75
-0.25x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.25x + x2 = 1.75

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 = 1.75 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1.75 + 0.015625

Combine like terms: 1.75 + 0.015625 = 1.765625
0.015625 + -0.25x + x2 = 1.765625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.328768227 and -1.328768227.

Subproblem 1
x + -0.125 = 1.328768227

Simplifying
x + -0.125 = 1.328768227

Reorder the terms:
-0.125 + x = 1.328768227

Solving
-0.125 + x = 1.328768227

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 = 1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.328768227 + 0.125
x = 1.328768227 + 0.125

Combine like terms: 1.328768227 + 0.125 = 1.453768227
x = 1.453768227

Simplifying
x = 1.453768227

Subproblem 2
x + -0.125 = -1.328768227

Simplifying
x + -0.125 = -1.328768227

Reorder the terms:
-0.125 + x = -1.328768227

Solving
-0.125 + x = -1.328768227

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 = -1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.328768227 + 0.125
x = -1.328768227 + 0.125

Combine like terms: -1.328768227 + 0.125 = -1.203768227
x = -1.203768227

Simplifying
x = -1.203768227

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.453768227, -1.203768227}
Solution
x = {1.453768227, -1.203768227}