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

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


Simplifying
(2x + 5y)(x + -1y) = 0

Multiply (2x + 5y) * (x + -1y)
(2x * (x + -1y) + 5y * (x + -1y)) = 0
((x * 2x + -1y * 2x) + 5y * (x + -1y)) = 0

Reorder the terms:
((-2xy + 2x2) + 5y * (x + -1y)) = 0
((-2xy + 2x2) + 5y * (x + -1y)) = 0
(-2xy + 2x2 + (x * 5y + -1y * 5y)) = 0
(-2xy + 2x2 + (5xy + -5y2)) = 0

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

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

Solving
3xy + 2x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(2x + 5y) = 0


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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

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

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {y, -2.5y}

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