(x+16)(x-18)=180

Solution for (x+16)(x-18)=180 equation:

Simplifying
(x + 16)(x + -18) = 180

Reorder the terms:
(16 + x)(x + -18) = 180

Reorder the terms:
(16 + x)(-18 + x) = 180

Multiply (16 + x) * (-18 + x)
(16(-18 + x) + x(-18 + x)) = 180
((-18 * 16 + x * 16) + x(-18 + x)) = 180
((-288 + 16x) + x(-18 + x)) = 180
(-288 + 16x + (-18 * x + x * x)) = 180
(-288 + 16x + (-18x + x2)) = 180

Combine like terms: 16x + -18x = -2x
(-288 + -2x + x2) = 180

Solving
-288 + -2x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-288 + -180 + -2x + x2 = 180 + -180

Combine like terms: -288 + -180 = -468
-468 + -2x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-468 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '468' to each side of the equation.
-468 + -2x + 468 + x2 = 0 + 468

Reorder the terms:
-468 + 468 + -2x + x2 = 0 + 468

Combine like terms: -468 + 468 = 0
0 + -2x + x2 = 0 + 468
-2x + x2 = 0 + 468

Combine like terms: 0 + 468 = 468
-2x + x2 = 468

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 468 + 1

Reorder the terms:
1 + -2x + x2 = 468 + 1

Combine like terms: 468 + 1 = 469
1 + -2x + x2 = 469

Factor a perfect square on the left side:
(x + -1)(x + -1) = 469

Calculate the square root of the right side: 21.656407828

Break this problem into two subproblems by setting 
(x + -1) equal to 21.656407828 and -21.656407828.

Subproblem 1
x + -1 = 21.656407828

Simplifying
x + -1 = 21.656407828

Reorder the terms:
-1 + x = 21.656407828

Solving
-1 + x = 21.656407828

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 21.656407828 + 1

Combine like terms: -1 + 1 = 0
0 + x = 21.656407828 + 1
x = 21.656407828 + 1

Combine like terms: 21.656407828 + 1 = 22.656407828
x = 22.656407828

Simplifying
x = 22.656407828

Subproblem 2
x + -1 = -21.656407828

Simplifying
x + -1 = -21.656407828

Reorder the terms:
-1 + x = -21.656407828

Solving
-1 + x = -21.656407828

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -21.656407828 + 1

Combine like terms: -1 + 1 = 0
0 + x = -21.656407828 + 1
x = -21.656407828 + 1

Combine like terms: -21.656407828 + 1 = -20.656407828
x = -20.656407828

Simplifying
x = -20.656407828

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.656407828, -20.656407828}