(4x-5y)(8x+y)=

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Solution for (4x-5y)(8x+y)= equation: 


Simplifying
(4x + -5y)(8x + y) = 0

Multiply (4x + -5y) * (8x + y)
(4x * (8x + y) + -5y * (8x + y)) = 0
((8x * 4x + y * 4x) + -5y * (8x + y)) = 0

Reorder the terms:
((4xy + 32x2) + -5y * (8x + y)) = 0
((4xy + 32x2) + -5y * (8x + y)) = 0
(4xy + 32x2 + (8x * -5y + y * -5y)) = 0
(4xy + 32x2 + (-40xy + -5y2)) = 0

Reorder the terms:
(4xy + -40xy + 32x2 + -5y2) = 0

Combine like terms: 4xy + -40xy = -36xy
(-36xy + 32x2 + -5y2) = 0

Solving
-36xy + 32x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -5y)(8x + 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 '(8x + y)' equal to zero and attempt to solve:

Simplifying
8x + y = 0

Solving
8x + y = 0

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

Add '-1y' to each side of the equation.
8x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
8x + 0 = 0 + -1y
8x = 0 + -1y
Remove the zero:
8x = -1y

Divide each side by '8'.
x = -0.125y

Simplifying
x = -0.125y
Solution
x = {1.25y, -0.125y}

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