180=(7x-1)(2x+1)

Solution for 180=(7x-1)(2x+1) equation:

Simplifying
180 = (7x + -1)(2x + 1)

Reorder the terms:
180 = (-1 + 7x)(2x + 1)

Reorder the terms:
180 = (-1 + 7x)(1 + 2x)

Multiply (-1 + 7x) * (1 + 2x)
180 = (-1(1 + 2x) + 7x * (1 + 2x))
180 = ((1 * -1 + 2x * -1) + 7x * (1 + 2x))
180 = ((-1 + -2x) + 7x * (1 + 2x))
180 = (-1 + -2x + (1 * 7x + 2x * 7x))
180 = (-1 + -2x + (7x + 14x2))

Combine like terms: -2x + 7x = 5x
180 = (-1 + 5x + 14x2)

Solving
180 = -1 + 5x + 14x2

Solving for variable 'x'.

Combine like terms: 180 + 1 = 181
181 + -5x + -14x2 = -1 + 5x + 14x2 + 1 + -5x + -14x2

Reorder the terms:
181 + -5x + -14x2 = -1 + 1 + 5x + -5x + 14x2 + -14x2

Combine like terms: -1 + 1 = 0
181 + -5x + -14x2 = 0 + 5x + -5x + 14x2 + -14x2
181 + -5x + -14x2 = 5x + -5x + 14x2 + -14x2

Combine like terms: 5x + -5x = 0
181 + -5x + -14x2 = 0 + 14x2 + -14x2
181 + -5x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
181 + -5x + -14x2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-12.92857143 + 0.3571428571x + x2 = 0

Move the constant term to the right:

Add '12.92857143' to each side of the equation.
-12.92857143 + 0.3571428571x + 12.92857143 + x2 = 0 + 12.92857143

Reorder the terms:
-12.92857143 + 12.92857143 + 0.3571428571x + x2 = 0 + 12.92857143

Combine like terms: -12.92857143 + 12.92857143 = 0.00000000
0.00000000 + 0.3571428571x + x2 = 0 + 12.92857143
0.3571428571x + x2 = 0 + 12.92857143

Combine like terms: 0 + 12.92857143 = 12.92857143
0.3571428571x + x2 = 12.92857143

The x term is 0.3571428571x.  Take half its coefficient (0.1785714286).
Square it (0.03188775511) and add it to both sides.

Add '0.03188775511' to each side of the equation.
0.3571428571x + 0.03188775511 + x2 = 12.92857143 + 0.03188775511

Reorder the terms:
0.03188775511 + 0.3571428571x + x2 = 12.92857143 + 0.03188775511

Combine like terms: 12.92857143 + 0.03188775511 = 12.96045918511
0.03188775511 + 0.3571428571x + x2 = 12.96045918511

Factor a perfect square on the left side:
(x + 0.1785714286)(x + 0.1785714286) = 12.96045918511

Calculate the square root of the right side: 3.600063775

Break this problem into two subproblems by setting 
(x + 0.1785714286) equal to 3.600063775 and -3.600063775.

Subproblem 1
x + 0.1785714286 = 3.600063775

Simplifying
x + 0.1785714286 = 3.600063775

Reorder the terms:
0.1785714286 + x = 3.600063775

Solving
0.1785714286 + x = 3.600063775

Solving for variable 'x'.

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

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -0.1785714286 + x = 3.600063775 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + x = 3.600063775 + -0.1785714286
x = 3.600063775 + -0.1785714286

Combine like terms: 3.600063775 + -0.1785714286 = 3.4214923464
x = 3.4214923464

Simplifying
x = 3.4214923464

Subproblem 2
x + 0.1785714286 = -3.600063775

Simplifying
x + 0.1785714286 = -3.600063775

Reorder the terms:
0.1785714286 + x = -3.600063775

Solving
0.1785714286 + x = -3.600063775

Solving for variable 'x'.

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

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -0.1785714286 + x = -3.600063775 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + x = -3.600063775 + -0.1785714286
x = -3.600063775 + -0.1785714286

Combine like terms: -3.600063775 + -0.1785714286 = -3.7786352036
x = -3.7786352036

Simplifying
x = -3.7786352036

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4214923464, -3.7786352036}