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

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


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

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

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

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

Combine like terms: 4xy + 5xy = 9xy
(9xy + 4x2 + 5y2) = 0

Solving
9xy + 4x2 + 5y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1y, -1.25y}

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