5x(-6x-7y)5y(3x+6y)=

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Solution for 5x(-6x-7y)5y(3x+6y)= equation: 


Simplifying
5x(-6x + -7y) * 5y(3x + 6y) = 0

Reorder the terms for easier multiplication:
5 * 5x * y(-6x + -7y)(3x + 6y) = 0

Multiply 5 * 5
25x * y(-6x + -7y)(3x + 6y) = 0

Multiply x * y
25xy(-6x + -7y)(3x + 6y) = 0

Multiply (-6x + -7y) * (3x + 6y)
25xy(-6x * (3x + 6y) + -7y * (3x + 6y)) = 0
25xy((3x * -6x + 6y * -6x) + -7y * (3x + 6y)) = 0

Reorder the terms:
25xy((-36xy + -18x2) + -7y * (3x + 6y)) = 0
25xy((-36xy + -18x2) + -7y * (3x + 6y)) = 0
25xy(-36xy + -18x2 + (3x * -7y + 6y * -7y)) = 0
25xy(-36xy + -18x2 + (-21xy + -42y2)) = 0

Reorder the terms:
25xy(-36xy + -21xy + -18x2 + -42y2) = 0

Combine like terms: -36xy + -21xy = -57xy
25xy(-57xy + -18x2 + -42y2) = 0
(-57xy * 25xy + -18x2 * 25xy + -42y2 * 25xy) = 0

Reorder the terms:
(-1050xy3 + -1425x2y2 + -450x3y) = 0
(-1050xy3 + -1425x2y2 + -450x3y) = 0

Solving
-1050xy3 + -1425x2y2 + -450x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-75xy'.
-75xy(14y2 + 19xy + 6x2) = 0

Factor a trinomial.
-75xy((2y + x)(7y + 6x)) = 0

Ignore the factor -75.

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 '(2y + x)' equal to zero and attempt to solve:

Simplifying
2y + x = 0

Reorder the terms:
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y

Subproblem 3
Set the factor '(7y + 6x)' equal to zero and attempt to solve:

Simplifying
7y + 6x = 0

Reorder the terms:
6x + 7y = 0

Solving
6x + 7y = 0

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

Add '-7y' to each side of the equation.
6x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
6x + 0 = 0 + -7y
6x = 0 + -7y
Remove the zero:
6x = -7y

Divide each side by '6'.
x = -1.166666667y

Simplifying
x = -1.166666667y
Solution
x = {-2y, -1.166666667y}

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