3(6x-4)(5x+1)=2

Solution for 3(6x-4)(5x+1)=2 equation:

Simplifying
3(6x + -4)(5x + 1) = 2

Reorder the terms:
3(-4 + 6x)(5x + 1) = 2

Reorder the terms:
3(-4 + 6x)(1 + 5x) = 2

Multiply (-4 + 6x) * (1 + 5x)
3(-4(1 + 5x) + 6x * (1 + 5x)) = 2
3((1 * -4 + 5x * -4) + 6x * (1 + 5x)) = 2
3((-4 + -20x) + 6x * (1 + 5x)) = 2
3(-4 + -20x + (1 * 6x + 5x * 6x)) = 2
3(-4 + -20x + (6x + 30x2)) = 2

Combine like terms: -20x + 6x = -14x
3(-4 + -14x + 30x2) = 2
(-4 * 3 + -14x * 3 + 30x2 * 3) = 2
(-12 + -42x + 90x2) = 2

Solving
-12 + -42x + 90x2 = 2

Solving for variable 'x'.

Reorder the terms:
-12 + -2 + -42x + 90x2 = 2 + -2

Combine like terms: -12 + -2 = -14
-14 + -42x + 90x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-14 + -42x + 90x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -21x + 45x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -21x + 45x2)' equal to zero and attempt to solve:

Simplifying
-7 + -21x + 45x2 = 0

Solving
-7 + -21x + 45x2 = 0

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

Divide each side by '45'.
-0.1555555556 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.1555555556' to each side of the equation.
-0.1555555556 + -0.4666666667x + 0.1555555556 + x2 = 0 + 0.1555555556

Reorder the terms:
-0.1555555556 + 0.1555555556 + -0.4666666667x + x2 = 0 + 0.1555555556

Combine like terms: -0.1555555556 + 0.1555555556 = 0.0000000000
0.0000000000 + -0.4666666667x + x2 = 0 + 0.1555555556
-0.4666666667x + x2 = 0 + 0.1555555556

Combine like terms: 0 + 0.1555555556 = 0.1555555556
-0.4666666667x + x2 = 0.1555555556

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 0.1555555556 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 0.1555555556 + 0.05444444448

Combine like terms: 0.1555555556 + 0.05444444448 = 0.21000000008
0.05444444448 + -0.4666666667x + x2 = 0.21000000008

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 0.21000000008

Calculate the square root of the right side: 0.45825757

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 0.45825757 and -0.45825757.

Subproblem 1
x + -0.2333333334 = 0.45825757

Simplifying
x + -0.2333333334 = 0.45825757

Reorder the terms:
-0.2333333334 + x = 0.45825757

Solving
-0.2333333334 + x = 0.45825757

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = 0.45825757 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = 0.45825757 + 0.2333333334
x = 0.45825757 + 0.2333333334

Combine like terms: 0.45825757 + 0.2333333334 = 0.6915909034
x = 0.6915909034

Simplifying
x = 0.6915909034

Subproblem 2
x + -0.2333333334 = -0.45825757

Simplifying
x + -0.2333333334 = -0.45825757

Reorder the terms:
-0.2333333334 + x = -0.45825757

Solving
-0.2333333334 + x = -0.45825757

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = -0.45825757 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = -0.45825757 + 0.2333333334
x = -0.45825757 + 0.2333333334

Combine like terms: -0.45825757 + 0.2333333334 = -0.2249242366
x = -0.2249242366

Simplifying
x = -0.2249242366

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6915909034, -0.2249242366}
Solution
x = {0.6915909034, -0.2249242366}