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

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


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

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

Reorder the terms:
((72xy + 45x2) + -9y * (5x + 8y)) = 0
((72xy + 45x2) + -9y * (5x + 8y)) = 0
(72xy + 45x2 + (5x * -9y + 8y * -9y)) = 0
(72xy + 45x2 + (-45xy + -72y2)) = 0

Reorder the terms:
(72xy + -45xy + 45x2 + -72y2) = 0

Combine like terms: 72xy + -45xy = 27xy
(27xy + 45x2 + -72y2) = 0

Solving
27xy + 45x2 + -72y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(3xy + 5x2 + -8y2) = 0

Factor a trinomial.
9((x + -1y)(5x + 8y)) = 0

Ignore the factor 9.

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 '(5x + 8y)' equal to zero and attempt to solve:

Simplifying
5x + 8y = 0

Solving
5x + 8y = 0

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

Add '-8y' to each side of the equation.
5x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
5x + 0 = 0 + -8y
5x = 0 + -8y
Remove the zero:
5x = -8y

Divide each side by '5'.
x = -1.6y

Simplifying
x = -1.6y
Solution
x = {y, -1.6y}

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