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

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

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

Reorder the terms:
7x(3 + x) = 3(x + -1)
(3 * 7x + x * 7x) = 3(x + -1)
(21x + 7x2) = 3(x + -1)

Reorder the terms:
21x + 7x2 = 3(-1 + x)
21x + 7x2 = (-1 * 3 + x * 3)
21x + 7x2 = (-3 + 3x)

Solving
21x + 7x2 = -3 + 3x

Solving for variable 'x'.

Reorder the terms:
3 + 21x + -3x + 7x2 = -3 + 3x + 3 + -3x

Combine like terms: 21x + -3x = 18x
3 + 18x + 7x2 = -3 + 3x + 3 + -3x

Reorder the terms:
3 + 18x + 7x2 = -3 + 3 + 3x + -3x

Combine like terms: -3 + 3 = 0
3 + 18x + 7x2 = 0 + 3x + -3x
3 + 18x + 7x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
3 + 18x + 7x2 = 0

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

Divide each side by '7'.
0.4285714286 + 2.571428571x + x2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + 2.571428571x + -0.4285714286 + x2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + 2.571428571x + x2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + 2.571428571x + x2 = 0 + -0.4285714286
2.571428571x + x2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
2.571428571x + x2 = -0.4285714286

The x term is 2.571428571x.  Take half its coefficient (1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
2.571428571x + 1.653061225 + x2 = -0.4285714286 + 1.653061225

Reorder the terms:
1.653061225 + 2.571428571x + x2 = -0.4285714286 + 1.653061225

Combine like terms: -0.4285714286 + 1.653061225 = 1.2244897964
1.653061225 + 2.571428571x + x2 = 1.2244897964

Factor a perfect square on the left side:
(x + 1.285714286)(x + 1.285714286) = 1.2244897964

Calculate the square root of the right side: 1.106566671

Break this problem into two subproblems by setting 
(x + 1.285714286) equal to 1.106566671 and -1.106566671.

Subproblem 1
x + 1.285714286 = 1.106566671

Simplifying
x + 1.285714286 = 1.106566671

Reorder the terms:
1.285714286 + x = 1.106566671

Solving
1.285714286 + x = 1.106566671

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x = 1.106566671 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x = 1.106566671 + -1.285714286
x = 1.106566671 + -1.285714286

Combine like terms: 1.106566671 + -1.285714286 = -0.179147615
x = -0.179147615

Simplifying
x = -0.179147615

Subproblem 2
x + 1.285714286 = -1.106566671

Simplifying
x + 1.285714286 = -1.106566671

Reorder the terms:
1.285714286 + x = -1.106566671

Solving
1.285714286 + x = -1.106566671

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x = -1.106566671 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x = -1.106566671 + -1.285714286
x = -1.106566671 + -1.285714286

Combine like terms: -1.106566671 + -1.285714286 = -2.392280957
x = -2.392280957

Simplifying
x = -2.392280957

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.179147615, -2.392280957}