(x-6y)(5x+4y)=0

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Solution for (x-6y)(5x+4y)=0 equation: 


Simplifying
(x + -6y)(5x + 4y) = 0

Multiply (x + -6y) * (5x + 4y)
(x(5x + 4y) + -6y * (5x + 4y)) = 0
((5x * x + 4y * x) + -6y * (5x + 4y)) = 0

Reorder the terms:
((4xy + 5x2) + -6y * (5x + 4y)) = 0
((4xy + 5x2) + -6y * (5x + 4y)) = 0
(4xy + 5x2 + (5x * -6y + 4y * -6y)) = 0
(4xy + 5x2 + (-30xy + -24y2)) = 0

Reorder the terms:
(4xy + -30xy + 5x2 + -24y2) = 0

Combine like terms: 4xy + -30xy = -26xy
(-26xy + 5x2 + -24y2) = 0

Solving
-26xy + 5x2 + -24y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -6y)(5x + 4y) = 0


Subproblem 1
Set the factor '(x + -6y)' equal to zero and attempt to solve:

Simplifying
x + -6y = 0

Solving
x + -6y = 0

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

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

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

Simplifying
x = 6y

Subproblem 2
Set the factor '(5x + 4y)' equal to zero and attempt to solve:

Simplifying
5x + 4y = 0

Solving
5x + 4y = 0

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

Add '-4y' to each side of the equation.
5x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
5x + 0 = 0 + -4y
5x = 0 + -4y
Remove the zero:
5x = -4y

Divide each side by '5'.
x = -0.8y

Simplifying
x = -0.8y
Solution
x = {6y, -0.8y}

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