(7x-2)(3x+1)=3(1-3x)

Solution for (7x-2)(3x+1)=3(1-3x) equation:

Simplifying
(7x + -2)(3x + 1) = 3(1 + -3x)

Reorder the terms:
(-2 + 7x)(3x + 1) = 3(1 + -3x)

Reorder the terms:
(-2 + 7x)(1 + 3x) = 3(1 + -3x)

Multiply (-2 + 7x) * (1 + 3x)
(-2(1 + 3x) + 7x * (1 + 3x)) = 3(1 + -3x)
((1 * -2 + 3x * -2) + 7x * (1 + 3x)) = 3(1 + -3x)
((-2 + -6x) + 7x * (1 + 3x)) = 3(1 + -3x)
(-2 + -6x + (1 * 7x + 3x * 7x)) = 3(1 + -3x)
(-2 + -6x + (7x + 21x2)) = 3(1 + -3x)

Combine like terms: -6x + 7x = 1x
(-2 + 1x + 21x2) = 3(1 + -3x)
-2 + 1x + 21x2 = (1 * 3 + -3x * 3)
-2 + 1x + 21x2 = (3 + -9x)

Solving
-2 + 1x + 21x2 = 3 + -9x

Solving for variable 'x'.

Reorder the terms:
-2 + -3 + 1x + 9x + 21x2 = 3 + -9x + -3 + 9x

Combine like terms: -2 + -3 = -5
-5 + 1x + 9x + 21x2 = 3 + -9x + -3 + 9x

Combine like terms: 1x + 9x = 10x
-5 + 10x + 21x2 = 3 + -9x + -3 + 9x

Reorder the terms:
-5 + 10x + 21x2 = 3 + -3 + -9x + 9x

Combine like terms: 3 + -3 = 0
-5 + 10x + 21x2 = 0 + -9x + 9x
-5 + 10x + 21x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-5 + 10x + 21x2 = 0

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

Divide each side by '21'.
-0.2380952381 + 0.4761904762x + x2 = 0

Move the constant term to the right:

Add '0.2380952381' to each side of the equation.
-0.2380952381 + 0.4761904762x + 0.2380952381 + x2 = 0 + 0.2380952381

Reorder the terms:
-0.2380952381 + 0.2380952381 + 0.4761904762x + x2 = 0 + 0.2380952381

Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000
0.0000000000 + 0.4761904762x + x2 = 0 + 0.2380952381
0.4761904762x + x2 = 0 + 0.2380952381

Combine like terms: 0 + 0.2380952381 = 0.2380952381
0.4761904762x + x2 = 0.2380952381

The x term is 0.4761904762x.  Take half its coefficient (0.2380952381).
Square it (0.05668934241) and add it to both sides.

Add '0.05668934241' to each side of the equation.
0.4761904762x + 0.05668934241 + x2 = 0.2380952381 + 0.05668934241

Reorder the terms:
0.05668934241 + 0.4761904762x + x2 = 0.2380952381 + 0.05668934241

Combine like terms: 0.2380952381 + 0.05668934241 = 0.29478458051
0.05668934241 + 0.4761904762x + x2 = 0.29478458051

Factor a perfect square on the left side:
(x + 0.2380952381)(x + 0.2380952381) = 0.29478458051

Calculate the square root of the right side: 0.542940679

Break this problem into two subproblems by setting 
(x + 0.2380952381) equal to 0.542940679 and -0.542940679.

Subproblem 1
x + 0.2380952381 = 0.542940679

Simplifying
x + 0.2380952381 = 0.542940679

Reorder the terms:
0.2380952381 + x = 0.542940679

Solving
0.2380952381 + x = 0.542940679

Solving for variable 'x'.

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

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -0.2380952381 + x = 0.542940679 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + x = 0.542940679 + -0.2380952381
x = 0.542940679 + -0.2380952381

Combine like terms: 0.542940679 + -0.2380952381 = 0.3048454409
x = 0.3048454409

Simplifying
x = 0.3048454409

Subproblem 2
x + 0.2380952381 = -0.542940679

Simplifying
x + 0.2380952381 = -0.542940679

Reorder the terms:
0.2380952381 + x = -0.542940679

Solving
0.2380952381 + x = -0.542940679

Solving for variable 'x'.

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

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -0.2380952381 + x = -0.542940679 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + x = -0.542940679 + -0.2380952381
x = -0.542940679 + -0.2380952381

Combine like terms: -0.542940679 + -0.2380952381 = -0.7810359171
x = -0.7810359171

Simplifying
x = -0.7810359171

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3048454409, -0.7810359171}