x(x+8)y=762*y

Solution for x(x+8)y=762*y equation:

Simplifying
x(x + 8) * y = 762y

Reorder the terms:
x(8 + x) * y = 762y

Reorder the terms for easier multiplication:
x * y(8 + x) = 762y

Multiply x * y
xy(8 + x) = 762y
(8 * xy + x * xy) = 762y
(8xy + x2y) = 762y

Solving
8xy + x2y = 762y

Solving for variable 'x'.

Combine like terms: 762y + -762y = 0
8xy + x2y + -762y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(8x + x2 + -762) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(8x + x2 + -762)' equal to zero and attempt to solve:

Simplifying
8x + x2 + -762 = 0

Reorder the terms:
-762 + 8x + x2 = 0

Solving
-762 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '762' to each side of the equation.
-762 + 8x + 762 + x2 = 0 + 762

Reorder the terms:
-762 + 762 + 8x + x2 = 0 + 762

Combine like terms: -762 + 762 = 0
0 + 8x + x2 = 0 + 762
8x + x2 = 0 + 762

Combine like terms: 0 + 762 = 762
8x + x2 = 762

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 762 + 16

Reorder the terms:
16 + 8x + x2 = 762 + 16

Combine like terms: 762 + 16 = 778
16 + 8x + x2 = 778

Factor a perfect square on the left side:
(x + 4)(x + 4) = 778

Calculate the square root of the right side: 27.892651362

Break this problem into two subproblems by setting 
(x + 4) equal to 27.892651362 and -27.892651362.

Subproblem 1
x + 4 = 27.892651362

Simplifying
x + 4 = 27.892651362

Reorder the terms:
4 + x = 27.892651362

Solving
4 + x = 27.892651362

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 27.892651362 + -4

Combine like terms: 4 + -4 = 0
0 + x = 27.892651362 + -4
x = 27.892651362 + -4

Combine like terms: 27.892651362 + -4 = 23.892651362
x = 23.892651362

Simplifying
x = 23.892651362

Subproblem 2
x + 4 = -27.892651362

Simplifying
x + 4 = -27.892651362

Reorder the terms:
4 + x = -27.892651362

Solving
4 + x = -27.892651362

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -27.892651362 + -4

Combine like terms: 4 + -4 = 0
0 + x = -27.892651362 + -4
x = -27.892651362 + -4

Combine like terms: -27.892651362 + -4 = -31.892651362
x = -31.892651362

Simplifying
x = -31.892651362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.892651362, -31.892651362}
Solution
x = {23.892651362, -31.892651362}