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

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


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

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

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

Reorder the terms:
(3xy + -25xy + 5x2 + -15y2) = 0

Combine like terms: 3xy + -25xy = -22xy
(-22xy + 5x2 + -15y2) = 0

Solving
-22xy + 5x2 + -15y2 = 0

Solving for variable 'x'.

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


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

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

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

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

Simplifying
x = 5y

Subproblem 2
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
Solution
x = {5y, -0.6y}

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