(x+2y)(x+5y)=

Solution for (x+2y)(x+5y)= equation:

Simplifying
(x + 2y)(x + 5y) = 0

Multiply (x + 2y) * (x + 5y)
(x(x + 5y) + 2y * (x + 5y)) = 0
((x * x + 5y * x) + 2y * (x + 5y)) = 0

Reorder the terms:
((5xy + x2) + 2y * (x + 5y)) = 0
((5xy + x2) + 2y * (x + 5y)) = 0
(5xy + x2 + (x * 2y + 5y * 2y)) = 0
(5xy + x2 + (2xy + 10y2)) = 0

Reorder the terms:
(5xy + 2xy + x2 + 10y2) = 0

Combine like terms: 5xy + 2xy = 7xy
(7xy + x2 + 10y2) = 0

Solving
7xy + x2 + 10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + 2y)(x + 5y) = 0

Subproblem 1
Set the factor '(x + 2y)' equal to zero and attempt to solve:

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
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 = {-2y, -5y}