(x+y)(4x-5y)=0

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Solution for (x+y)(4x-5y)=0 equation: 


Simplifying
(x + y)(4x + -5y) = 0

Multiply (x + y) * (4x + -5y)
(x(4x + -5y) + y(4x + -5y)) = 0
((4x * x + -5y * x) + y(4x + -5y)) = 0

Reorder the terms:
((-5xy + 4x2) + y(4x + -5y)) = 0
((-5xy + 4x2) + y(4x + -5y)) = 0
(-5xy + 4x2 + (4x * y + -5y * y)) = 0
(-5xy + 4x2 + (4xy + -5y2)) = 0

Reorder the terms:
(-5xy + 4xy + 4x2 + -5y2) = 0

Combine like terms: -5xy + 4xy = -1xy
(-1xy + 4x2 + -5y2) = 0

Solving
-1xy + 4x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -5y)(x + y) = 0


Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve:

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

Add '5y' to each side of the equation.
4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4x + 0 = 0 + 5y
4x = 0 + 5y
Remove the zero:
4x = 5y

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {1.25y, -1y}

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