(x-8)(x+9)=-2(x-33)

Solution for (x-8)(x+9)=-2(x-33) equation:

Simplifying
(x + -8)(x + 9) = -2(x + -33)

Reorder the terms:
(-8 + x)(x + 9) = -2(x + -33)

Reorder the terms:
(-8 + x)(9 + x) = -2(x + -33)

Multiply (-8 + x) * (9 + x)
(-8(9 + x) + x(9 + x)) = -2(x + -33)
((9 * -8 + x * -8) + x(9 + x)) = -2(x + -33)
((-72 + -8x) + x(9 + x)) = -2(x + -33)
(-72 + -8x + (9 * x + x * x)) = -2(x + -33)
(-72 + -8x + (9x + x2)) = -2(x + -33)

Combine like terms: -8x + 9x = 1x
(-72 + 1x + x2) = -2(x + -33)

Reorder the terms:
-72 + 1x + x2 = -2(-33 + x)
-72 + 1x + x2 = (-33 * -2 + x * -2)
-72 + 1x + x2 = (66 + -2x)

Solving
-72 + 1x + x2 = 66 + -2x

Solving for variable 'x'.

Reorder the terms:
-72 + -66 + 1x + 2x + x2 = 66 + -2x + -66 + 2x

Combine like terms: -72 + -66 = -138
-138 + 1x + 2x + x2 = 66 + -2x + -66 + 2x

Combine like terms: 1x + 2x = 3x
-138 + 3x + x2 = 66 + -2x + -66 + 2x

Reorder the terms:
-138 + 3x + x2 = 66 + -66 + -2x + 2x

Combine like terms: 66 + -66 = 0
-138 + 3x + x2 = 0 + -2x + 2x
-138 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-138 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '138' to each side of the equation.
-138 + 3x + 138 + x2 = 0 + 138

Reorder the terms:
-138 + 138 + 3x + x2 = 0 + 138

Combine like terms: -138 + 138 = 0
0 + 3x + x2 = 0 + 138
3x + x2 = 0 + 138

Combine like terms: 0 + 138 = 138
3x + x2 = 138

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 = 138 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 138 + 2.25

Combine like terms: 138 + 2.25 = 140.25
2.25 + 3x + x2 = 140.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11.842719282 and -11.842719282.

Subproblem 1
x + 1.5 = 11.842719282

Simplifying
x + 1.5 = 11.842719282

Reorder the terms:
1.5 + x = 11.842719282

Solving
1.5 + x = 11.842719282

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 = 11.842719282 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 11.842719282 + -1.5
x = 11.842719282 + -1.5

Combine like terms: 11.842719282 + -1.5 = 10.342719282
x = 10.342719282

Simplifying
x = 10.342719282

Subproblem 2
x + 1.5 = -11.842719282

Simplifying
x + 1.5 = -11.842719282

Reorder the terms:
1.5 + x = -11.842719282

Solving
1.5 + x = -11.842719282

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 = -11.842719282 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -11.842719282 + -1.5
x = -11.842719282 + -1.5

Combine like terms: -11.842719282 + -1.5 = -13.342719282
x = -13.342719282

Simplifying
x = -13.342719282

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.342719282, -13.342719282}