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

Subproblem 1
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
Subproblem 2
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
Solution
x = {3y, -5y}