(x+y)(x-72y)=

Solution for (x+y)(x-72y)= equation:

Simplifying
(x + y)(x + -72y) = 0

Multiply (x + y) * (x + -72y)
(x(x + -72y) + y(x + -72y)) = 0
((x * x + -72y * x) + y(x + -72y)) = 0

Reorder the terms:
((-72xy + x2) + y(x + -72y)) = 0
((-72xy + x2) + y(x + -72y)) = 0
(-72xy + x2 + (x * y + -72y * y)) = 0
(-72xy + x2 + (xy + -72y2)) = 0

Reorder the terms:
(-72xy + xy + x2 + -72y2) = 0

Combine like terms: -72xy + xy = -71xy
(-71xy + x2 + -72y2) = 0

Solving
-71xy + x2 + -72y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -72y)(x + y) = 0

Subproblem 1
Set the factor '(x + -72y)' equal to zero and attempt to solve:

Simplifying
x + -72y = 0

Solving
x + -72y = 0

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

Add '72y' to each side of the equation.
x + -72y + 72y = 0 + 72y

Combine like terms: -72y + 72y = 0
x + 0 = 0 + 72y
x = 0 + 72y
Remove the zero:
x = 72y

Simplifying
x = 72y
Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {72y, -1y}