(x+3y)(x-5y)=

Solution for (x+3y)(x-5y)= equation:

Simplifying
(x + 3y)(x + -5y) = 0

Multiply (x + 3y) * (x + -5y)
(x(x + -5y) + 3y * (x + -5y)) = 0
((x * x + -5y * x) + 3y * (x + -5y)) = 0

Reorder the terms:
((-5xy + x2) + 3y * (x + -5y)) = 0
((-5xy + x2) + 3y * (x + -5y)) = 0
(-5xy + x2 + (x * 3y + -5y * 3y)) = 0
(-5xy + x2 + (3xy + -15y2)) = 0

Reorder the terms:
(-5xy + 3xy + x2 + -15y2) = 0

Combine like terms: -5xy + 3xy = -2xy
(-2xy + x2 + -15y2) = 0

Solving
-2xy + x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(x + 3y) = 0

Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

Add '5y' to each side of the equation.
x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x + 0 = 0 + 5y
x = 0 + 5y
Remove the zero:
x = 5y

Simplifying
x = 5y
Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y
Solution
x = {5y, -3y}