(2x+7y)(5x-6y)=0

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Solution for (2x+7y)(5x-6y)=0 equation: 


Simplifying
(2x + 7y)(5x + -6y) = 0

Multiply (2x + 7y) * (5x + -6y)
(2x * (5x + -6y) + 7y * (5x + -6y)) = 0
((5x * 2x + -6y * 2x) + 7y * (5x + -6y)) = 0

Reorder the terms:
((-12xy + 10x2) + 7y * (5x + -6y)) = 0
((-12xy + 10x2) + 7y * (5x + -6y)) = 0
(-12xy + 10x2 + (5x * 7y + -6y * 7y)) = 0
(-12xy + 10x2 + (35xy + -42y2)) = 0

Reorder the terms:
(-12xy + 35xy + 10x2 + -42y2) = 0

Combine like terms: -12xy + 35xy = 23xy
(23xy + 10x2 + -42y2) = 0

Solving
23xy + 10x2 + -42y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -6y)(2x + 7y) = 0


Subproblem 1
Set the factor '(5x + -6y)' equal to zero and attempt to solve:

Simplifying
5x + -6y = 0

Solving
5x + -6y = 0

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

Add '6y' to each side of the equation.
5x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
5x + 0 = 0 + 6y
5x = 0 + 6y
Remove the zero:
5x = 6y

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y

Subproblem 2
Set the factor '(2x + 7y)' equal to zero and attempt to solve:

Simplifying
2x + 7y = 0

Solving
2x + 7y = 0

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

Add '-7y' to each side of the equation.
2x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
2x + 0 = 0 + -7y
2x = 0 + -7y
Remove the zero:
2x = -7y

Divide each side by '2'.
x = -3.5y

Simplifying
x = -3.5y
Solution
x = {1.2y, -3.5y}

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