25xy(2x+5y)=75xy(5x+2y)

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Solution for 25xy(2x+5y)=75xy(5x+2y) equation: 


Simplifying
25xy(2x + 5y) = 75xy(5x + 2y)
(2x * 25xy + 5y * 25xy) = 75xy(5x + 2y)

Reorder the terms:
(125xy2 + 50x2y) = 75xy(5x + 2y)
(125xy2 + 50x2y) = 75xy(5x + 2y)
125xy2 + 50x2y = (5x * 75xy + 2y * 75xy)

Reorder the terms:
125xy2 + 50x2y = (150xy2 + 375x2y)
125xy2 + 50x2y = (150xy2 + 375x2y)

Solving
125xy2 + 50x2y = 150xy2 + 375x2y

Solving for variable 'x'.

Reorder the terms:
125xy2 + -150xy2 + 50x2y + -375x2y = 150xy2 + 375x2y + -150xy2 + -375x2y

Combine like terms: 125xy2 + -150xy2 = -25xy2
-25xy2 + 50x2y + -375x2y = 150xy2 + 375x2y + -150xy2 + -375x2y

Combine like terms: 50x2y + -375x2y = -325x2y
-25xy2 + -325x2y = 150xy2 + 375x2y + -150xy2 + -375x2y

Reorder the terms:
-25xy2 + -325x2y = 150xy2 + -150xy2 + 375x2y + -375x2y

Combine like terms: 150xy2 + -150xy2 = 0
-25xy2 + -325x2y = 0 + 375x2y + -375x2y
-25xy2 + -325x2y = 375x2y + -375x2y

Combine like terms: 375x2y + -375x2y = 0
-25xy2 + -325x2y = 0

Factor out the Greatest Common Factor (GCF), '-25xy'.
-25xy(y + 13x) = 0

Ignore the factor -25.

Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve:

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(y + 13x)' equal to zero and attempt to solve:

Simplifying
y + 13x = 0

Reorder the terms:
13x + y = 0

Solving
13x + y = 0

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

Add '-1y' to each side of the equation.
13x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
13x + 0 = 0 + -1y
13x = 0 + -1y
Remove the zero:
13x = -1y

Divide each side by '13'.
x = -0.07692307692y

Simplifying
x = -0.07692307692y
Solution
x = {-0.07692307692y}

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