(5x-3y)(5x+8y)=

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Solution for (5x-3y)(5x+8y)= equation: 


Simplifying
(5x + -3y)(5x + 8y) = 0

Multiply (5x + -3y) * (5x + 8y)
(5x * (5x + 8y) + -3y * (5x + 8y)) = 0
((5x * 5x + 8y * 5x) + -3y * (5x + 8y)) = 0

Reorder the terms:
((40xy + 25x2) + -3y * (5x + 8y)) = 0
((40xy + 25x2) + -3y * (5x + 8y)) = 0
(40xy + 25x2 + (5x * -3y + 8y * -3y)) = 0
(40xy + 25x2 + (-15xy + -24y2)) = 0

Reorder the terms:
(40xy + -15xy + 25x2 + -24y2) = 0

Combine like terms: 40xy + -15xy = 25xy
(25xy + 25x2 + -24y2) = 0

Solving
25xy + 25x2 + -24y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -3y)(5x + 8y) = 0


Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

Add '3y' to each side of the equation.
5x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 = 0 + 3y
5x = 0 + 3y
Remove the zero:
5x = 3y

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y

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 = {0.6y, -1.6y}

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