(4x+5y)(8x-9y)=

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Solution for (4x+5y)(8x-9y)= equation: 


Simplifying
(4x + 5y)(8x + -9y) = 0

Multiply (4x + 5y) * (8x + -9y)
(4x * (8x + -9y) + 5y * (8x + -9y)) = 0
((8x * 4x + -9y * 4x) + 5y * (8x + -9y)) = 0

Reorder the terms:
((-36xy + 32x2) + 5y * (8x + -9y)) = 0
((-36xy + 32x2) + 5y * (8x + -9y)) = 0
(-36xy + 32x2 + (8x * 5y + -9y * 5y)) = 0
(-36xy + 32x2 + (40xy + -45y2)) = 0

Reorder the terms:
(-36xy + 40xy + 32x2 + -45y2) = 0

Combine like terms: -36xy + 40xy = 4xy
(4xy + 32x2 + -45y2) = 0

Solving
4xy + 32x2 + -45y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8x + -9y)(4x + 5y) = 0


Subproblem 1
Set the factor '(8x + -9y)' equal to zero and attempt to solve:

Simplifying
8x + -9y = 0

Solving
8x + -9y = 0

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

Add '9y' to each side of the equation.
8x + -9y + 9y = 0 + 9y

Combine like terms: -9y + 9y = 0
8x + 0 = 0 + 9y
8x = 0 + 9y
Remove the zero:
8x = 9y

Divide each side by '8'.
x = 1.125y

Simplifying
x = 1.125y

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 = {1.125y, -1.25y}

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