(x-3)(x+6)=18(28)

Solution for (x-3)(x+6)=18(28) equation:

Simplifying
(x + -3)(x + 6) = 18(28)

Reorder the terms:
(-3 + x)(x + 6) = 18(28)

Reorder the terms:
(-3 + x)(6 + x) = 18(28)

Multiply (-3 + x) * (6 + x)
(-3(6 + x) + x(6 + x)) = 18(28)
((6 * -3 + x * -3) + x(6 + x)) = 18(28)
((-18 + -3x) + x(6 + x)) = 18(28)
(-18 + -3x + (6 * x + x * x)) = 18(28)
(-18 + -3x + (6x + x2)) = 18(28)

Combine like terms: -3x + 6x = 3x
(-18 + 3x + x2) = 18(28)

Multiply 18 * 28
-18 + 3x + x2 = 504

Solving
-18 + 3x + x2 = 504

Solving for variable 'x'.

Reorder the terms:
-18 + -504 + 3x + x2 = 504 + -504

Combine like terms: -18 + -504 = -522
-522 + 3x + x2 = 504 + -504

Combine like terms: 504 + -504 = 0
-522 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '522' to each side of the equation.
-522 + 3x + 522 + x2 = 0 + 522

Reorder the terms:
-522 + 522 + 3x + x2 = 0 + 522

Combine like terms: -522 + 522 = 0
0 + 3x + x2 = 0 + 522
3x + x2 = 0 + 522

Combine like terms: 0 + 522 = 522
3x + x2 = 522

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 522 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 522 + 2.25

Combine like terms: 522 + 2.25 = 524.25
2.25 + 3x + x2 = 524.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 524.25

Calculate the square root of the right side: 22.896506284

Break this problem into two subproblems by setting 
(x + 1.5) equal to 22.896506284 and -22.896506284.

Subproblem 1
x + 1.5 = 22.896506284

Simplifying
x + 1.5 = 22.896506284

Reorder the terms:
1.5 + x = 22.896506284

Solving
1.5 + x = 22.896506284

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 22.896506284 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 22.896506284 + -1.5
x = 22.896506284 + -1.5

Combine like terms: 22.896506284 + -1.5 = 21.396506284
x = 21.396506284

Simplifying
x = 21.396506284

Subproblem 2
x + 1.5 = -22.896506284

Simplifying
x + 1.5 = -22.896506284

Reorder the terms:
1.5 + x = -22.896506284

Solving
1.5 + x = -22.896506284

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -22.896506284 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -22.896506284 + -1.5
x = -22.896506284 + -1.5

Combine like terms: -22.896506284 + -1.5 = -24.396506284
x = -24.396506284

Simplifying
x = -24.396506284

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.396506284, -24.396506284}