(x+5y)(x-12y)=

Solution for (x+5y)(x-12y)= equation:

Simplifying
(x + 5y)(x + -12y) = 0

Multiply (x + 5y) * (x + -12y)
(x(x + -12y) + 5y * (x + -12y)) = 0
((x * x + -12y * x) + 5y * (x + -12y)) = 0

Reorder the terms:
((-12xy + x2) + 5y * (x + -12y)) = 0
((-12xy + x2) + 5y * (x + -12y)) = 0
(-12xy + x2 + (x * 5y + -12y * 5y)) = 0
(-12xy + x2 + (5xy + -60y2)) = 0

Reorder the terms:
(-12xy + 5xy + x2 + -60y2) = 0

Combine like terms: -12xy + 5xy = -7xy
(-7xy + x2 + -60y2) = 0

Solving
-7xy + x2 + -60y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -12y)(x + 5y) = 0

Subproblem 1
Set the factor '(x + -12y)' equal to zero and attempt to solve:

Simplifying
x + -12y = 0

Solving
x + -12y = 0

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

Add '12y' to each side of the equation.
x + -12y + 12y = 0 + 12y

Combine like terms: -12y + 12y = 0
x + 0 = 0 + 12y
x = 0 + 12y
Remove the zero:
x = 12y

Simplifying
x = 12y
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 = {12y, -5y}