(x+58)(x+21)=180

Solution for (x+58)(x+21)=180 equation:

Simplifying
(x + 58)(x + 21) = 180

Reorder the terms:
(58 + x)(x + 21) = 180

Reorder the terms:
(58 + x)(21 + x) = 180

Multiply (58 + x) * (21 + x)
(58(21 + x) + x(21 + x)) = 180
((21 * 58 + x * 58) + x(21 + x)) = 180
((1218 + 58x) + x(21 + x)) = 180
(1218 + 58x + (21 * x + x * x)) = 180
(1218 + 58x + (21x + x2)) = 180

Combine like terms: 58x + 21x = 79x
(1218 + 79x + x2) = 180

Solving
1218 + 79x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
1218 + -180 + 79x + x2 = 180 + -180

Combine like terms: 1218 + -180 = 1038
1038 + 79x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
1038 + 79x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1038' to each side of the equation.
1038 + 79x + -1038 + x2 = 0 + -1038

Reorder the terms:
1038 + -1038 + 79x + x2 = 0 + -1038

Combine like terms: 1038 + -1038 = 0
0 + 79x + x2 = 0 + -1038
79x + x2 = 0 + -1038

Combine like terms: 0 + -1038 = -1038
79x + x2 = -1038

The x term is 79x.  Take half its coefficient (39.5).
Square it (1560.25) and add it to both sides.

Add '1560.25' to each side of the equation.
79x + 1560.25 + x2 = -1038 + 1560.25

Reorder the terms:
1560.25 + 79x + x2 = -1038 + 1560.25

Combine like terms: -1038 + 1560.25 = 522.25
1560.25 + 79x + x2 = 522.25

Factor a perfect square on the left side:
(x + 39.5)(x + 39.5) = 522.25

Calculate the square root of the right side: 22.852789764

Break this problem into two subproblems by setting 
(x + 39.5) equal to 22.852789764 and -22.852789764.

Subproblem 1
x + 39.5 = 22.852789764

Simplifying
x + 39.5 = 22.852789764

Reorder the terms:
39.5 + x = 22.852789764

Solving
39.5 + x = 22.852789764

Solving for variable 'x'.

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

Add '-39.5' to each side of the equation.
39.5 + -39.5 + x = 22.852789764 + -39.5

Combine like terms: 39.5 + -39.5 = 0.0
0.0 + x = 22.852789764 + -39.5
x = 22.852789764 + -39.5

Combine like terms: 22.852789764 + -39.5 = -16.647210236
x = -16.647210236

Simplifying
x = -16.647210236

Subproblem 2
x + 39.5 = -22.852789764

Simplifying
x + 39.5 = -22.852789764

Reorder the terms:
39.5 + x = -22.852789764

Solving
39.5 + x = -22.852789764

Solving for variable 'x'.

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

Add '-39.5' to each side of the equation.
39.5 + -39.5 + x = -22.852789764 + -39.5

Combine like terms: 39.5 + -39.5 = 0.0
0.0 + x = -22.852789764 + -39.5
x = -22.852789764 + -39.5

Combine like terms: -22.852789764 + -39.5 = -62.352789764
x = -62.352789764

Simplifying
x = -62.352789764

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-16.647210236, -62.352789764}