180=(2x+1)(3x+10)

Solution for 180=(2x+1)(3x+10) equation:

Simplifying
180 = (2x + 1)(3x + 10)

Reorder the terms:
180 = (1 + 2x)(3x + 10)

Reorder the terms:
180 = (1 + 2x)(10 + 3x)

Multiply (1 + 2x) * (10 + 3x)
180 = (1(10 + 3x) + 2x * (10 + 3x))
180 = ((10 * 1 + 3x * 1) + 2x * (10 + 3x))
180 = ((10 + 3x) + 2x * (10 + 3x))
180 = (10 + 3x + (10 * 2x + 3x * 2x))
180 = (10 + 3x + (20x + 6x2))

Combine like terms: 3x + 20x = 23x
180 = (10 + 23x + 6x2)

Solving
180 = 10 + 23x + 6x2

Solving for variable 'x'.

Combine like terms: 180 + -10 = 170
170 + -23x + -6x2 = 10 + 23x + 6x2 + -10 + -23x + -6x2

Reorder the terms:
170 + -23x + -6x2 = 10 + -10 + 23x + -23x + 6x2 + -6x2

Combine like terms: 10 + -10 = 0
170 + -23x + -6x2 = 0 + 23x + -23x + 6x2 + -6x2
170 + -23x + -6x2 = 23x + -23x + 6x2 + -6x2

Combine like terms: 23x + -23x = 0
170 + -23x + -6x2 = 0 + 6x2 + -6x2
170 + -23x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
170 + -23x + -6x2 = 0

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

Divide each side by '-6'.
-28.33333333 + 3.833333333x + x2 = 0

Move the constant term to the right:

Add '28.33333333' to each side of the equation.
-28.33333333 + 3.833333333x + 28.33333333 + x2 = 0 + 28.33333333

Reorder the terms:
-28.33333333 + 28.33333333 + 3.833333333x + x2 = 0 + 28.33333333

Combine like terms: -28.33333333 + 28.33333333 = 0.00000000
0.00000000 + 3.833333333x + x2 = 0 + 28.33333333
3.833333333x + x2 = 0 + 28.33333333

Combine like terms: 0 + 28.33333333 = 28.33333333
3.833333333x + x2 = 28.33333333

The x term is 3.833333333x.  Take half its coefficient (1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
3.833333333x + 3.673611112 + x2 = 28.33333333 + 3.673611112

Reorder the terms:
3.673611112 + 3.833333333x + x2 = 28.33333333 + 3.673611112

Combine like terms: 28.33333333 + 3.673611112 = 32.006944442
3.673611112 + 3.833333333x + x2 = 32.006944442

Factor a perfect square on the left side:
(x + 1.916666667)(x + 1.916666667) = 32.006944442

Calculate the square root of the right side: 5.657468024

Break this problem into two subproblems by setting 
(x + 1.916666667) equal to 5.657468024 and -5.657468024.

Subproblem 1
x + 1.916666667 = 5.657468024

Simplifying
x + 1.916666667 = 5.657468024

Reorder the terms:
1.916666667 + x = 5.657468024

Solving
1.916666667 + x = 5.657468024

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = 5.657468024 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = 5.657468024 + -1.916666667
x = 5.657468024 + -1.916666667

Combine like terms: 5.657468024 + -1.916666667 = 3.740801357
x = 3.740801357

Simplifying
x = 3.740801357

Subproblem 2
x + 1.916666667 = -5.657468024

Simplifying
x + 1.916666667 = -5.657468024

Reorder the terms:
1.916666667 + x = -5.657468024

Solving
1.916666667 + x = -5.657468024

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = -5.657468024 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = -5.657468024 + -1.916666667
x = -5.657468024 + -1.916666667

Combine like terms: -5.657468024 + -1.916666667 = -7.574134691
x = -7.574134691

Simplifying
x = -7.574134691

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.740801357, -7.574134691}