(5y+2x)(5y-3x)=0

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Solution for (5y+2x)(5y-3x)=0 equation: 


Simplifying
(5y + 2x)(5y + -3x) = 0

Reorder the terms:
(2x + 5y)(5y + -3x) = 0

Reorder the terms:
(2x + 5y)(-3x + 5y) = 0

Multiply (2x + 5y) * (-3x + 5y)
(2x * (-3x + 5y) + 5y * (-3x + 5y)) = 0
((-3x * 2x + 5y * 2x) + 5y * (-3x + 5y)) = 0

Reorder the terms:
((10xy + -6x2) + 5y * (-3x + 5y)) = 0
((10xy + -6x2) + 5y * (-3x + 5y)) = 0
(10xy + -6x2 + (-3x * 5y + 5y * 5y)) = 0
(10xy + -6x2 + (-15xy + 25y2)) = 0

Reorder the terms:
(10xy + -15xy + -6x2 + 25y2) = 0

Combine like terms: 10xy + -15xy = -5xy
(-5xy + -6x2 + 25y2) = 0

Solving
-5xy + -6x2 + 25y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2x + -5y)(3x + -5y) = 0


Subproblem 1
Set the factor '(-2x + -5y)' equal to zero and attempt to solve:

Simplifying
-2x + -5y = 0

Solving
-2x + -5y = 0

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

Add '5y' to each side of the equation.
-2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-2x + 0 = 0 + 5y
-2x = 0 + 5y
Remove the zero:
-2x = 5y

Divide each side by '-2'.
x = -2.5y

Simplifying
x = -2.5y

Subproblem 2
Set the factor '(3x + -5y)' equal to zero and attempt to solve:

Simplifying
3x + -5y = 0

Solving
3x + -5y = 0

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

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

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

Divide each side by '3'.
x = 1.666666667y

Simplifying
x = 1.666666667y
Solution
x = {-2.5y, 1.666666667y}

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