8(x-9)=-2x(x+41)

Solution for 8(x-9)=-2x(x+41) equation:

Simplifying
8(x + -9) = -2x(x + 41)

Reorder the terms:
8(-9 + x) = -2x(x + 41)
(-9 * 8 + x * 8) = -2x(x + 41)
(-72 + 8x) = -2x(x + 41)

Reorder the terms:
-72 + 8x = -2x(41 + x)
-72 + 8x = (41 * -2x + x * -2x)
-72 + 8x = (-82x + -2x2)

Solving
-72 + 8x = -82x + -2x2

Solving for variable 'x'.

Combine like terms: 8x + 82x = 90x
-72 + 90x + 2x2 = -82x + -2x2 + 82x + 2x2

Reorder the terms:
-72 + 90x + 2x2 = -82x + 82x + -2x2 + 2x2

Combine like terms: -82x + 82x = 0
-72 + 90x + 2x2 = 0 + -2x2 + 2x2
-72 + 90x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-72 + 90x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 45x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-36 + 45x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 45x + x2 = 0

Solving
-36 + 45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 45x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 45x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 45x + x2 = 0 + 36
45x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
45x + x2 = 36

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 36 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 36 + 506.25

Combine like terms: 36 + 506.25 = 542.25
506.25 + 45x + x2 = 542.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 542.25

Calculate the square root of the right side: 23.286262044

Break this problem into two subproblems by setting 
(x + 22.5) equal to 23.286262044 and -23.286262044.

Subproblem 1
x + 22.5 = 23.286262044

Simplifying
x + 22.5 = 23.286262044

Reorder the terms:
22.5 + x = 23.286262044

Solving
22.5 + x = 23.286262044

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 23.286262044 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 23.286262044 + -22.5
x = 23.286262044 + -22.5

Combine like terms: 23.286262044 + -22.5 = 0.786262044
x = 0.786262044

Simplifying
x = 0.786262044

Subproblem 2
x + 22.5 = -23.286262044

Simplifying
x + 22.5 = -23.286262044

Reorder the terms:
22.5 + x = -23.286262044

Solving
22.5 + x = -23.286262044

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -23.286262044 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -23.286262044 + -22.5
x = -23.286262044 + -22.5

Combine like terms: -23.286262044 + -22.5 = -45.786262044
x = -45.786262044

Simplifying
x = -45.786262044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.786262044, -45.786262044}
Solution
x = {0.786262044, -45.786262044}