180=(2x+1)(3x-31)

Solution for 180=(2x+1)(3x-31) equation:

Simplifying
180 = (2x + 1)(3x + -31)

Reorder the terms:
180 = (1 + 2x)(3x + -31)

Reorder the terms:
180 = (1 + 2x)(-31 + 3x)

Multiply (1 + 2x) * (-31 + 3x)
180 = (1(-31 + 3x) + 2x * (-31 + 3x))
180 = ((-31 * 1 + 3x * 1) + 2x * (-31 + 3x))
180 = ((-31 + 3x) + 2x * (-31 + 3x))
180 = (-31 + 3x + (-31 * 2x + 3x * 2x))
180 = (-31 + 3x + (-62x + 6x2))

Combine like terms: 3x + -62x = -59x
180 = (-31 + -59x + 6x2)

Solving
180 = -31 + -59x + 6x2

Solving for variable 'x'.

Combine like terms: 180 + 31 = 211
211 + 59x + -6x2 = -31 + -59x + 6x2 + 31 + 59x + -6x2

Reorder the terms:
211 + 59x + -6x2 = -31 + 31 + -59x + 59x + 6x2 + -6x2

Combine like terms: -31 + 31 = 0
211 + 59x + -6x2 = 0 + -59x + 59x + 6x2 + -6x2
211 + 59x + -6x2 = -59x + 59x + 6x2 + -6x2

Combine like terms: -59x + 59x = 0
211 + 59x + -6x2 = 0 + 6x2 + -6x2
211 + 59x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
211 + 59x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-35.16666667 + -9.833333333x + x2 = 0

Move the constant term to the right:

Add '35.16666667' to each side of the equation.
-35.16666667 + -9.833333333x + 35.16666667 + x2 = 0 + 35.16666667

Reorder the terms:
-35.16666667 + 35.16666667 + -9.833333333x + x2 = 0 + 35.16666667

Combine like terms: -35.16666667 + 35.16666667 = 0.00000000
0.00000000 + -9.833333333x + x2 = 0 + 35.16666667
-9.833333333x + x2 = 0 + 35.16666667

Combine like terms: 0 + 35.16666667 = 35.16666667
-9.833333333x + x2 = 35.16666667

The x term is -9.833333333x.  Take half its coefficient (-4.916666667).
Square it (24.17361111) and add it to both sides.

Add '24.17361111' to each side of the equation.
-9.833333333x + 24.17361111 + x2 = 35.16666667 + 24.17361111

Reorder the terms:
24.17361111 + -9.833333333x + x2 = 35.16666667 + 24.17361111

Combine like terms: 35.16666667 + 24.17361111 = 59.34027778
24.17361111 + -9.833333333x + x2 = 59.34027778

Factor a perfect square on the left side:
(x + -4.916666667)(x + -4.916666667) = 59.34027778

Calculate the square root of the right side: 7.703264099

Break this problem into two subproblems by setting 
(x + -4.916666667) equal to 7.703264099 and -7.703264099.

Subproblem 1
x + -4.916666667 = 7.703264099

Simplifying
x + -4.916666667 = 7.703264099

Reorder the terms:
-4.916666667 + x = 7.703264099

Solving
-4.916666667 + x = 7.703264099

Solving for variable 'x'.

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

Add '4.916666667' to each side of the equation.
-4.916666667 + 4.916666667 + x = 7.703264099 + 4.916666667

Combine like terms: -4.916666667 + 4.916666667 = 0.000000000
0.000000000 + x = 7.703264099 + 4.916666667
x = 7.703264099 + 4.916666667

Combine like terms: 7.703264099 + 4.916666667 = 12.619930766
x = 12.619930766

Simplifying
x = 12.619930766

Subproblem 2
x + -4.916666667 = -7.703264099

Simplifying
x + -4.916666667 = -7.703264099

Reorder the terms:
-4.916666667 + x = -7.703264099

Solving
-4.916666667 + x = -7.703264099

Solving for variable 'x'.

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

Add '4.916666667' to each side of the equation.
-4.916666667 + 4.916666667 + x = -7.703264099 + 4.916666667

Combine like terms: -4.916666667 + 4.916666667 = 0.000000000
0.000000000 + x = -7.703264099 + 4.916666667
x = -7.703264099 + 4.916666667

Combine like terms: -7.703264099 + 4.916666667 = -2.786597432
x = -2.786597432

Simplifying
x = -2.786597432

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.619930766, -2.786597432}