(4y-5x)(2y+7x)=

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Solution for (4y-5x)(2y+7x)= equation: 


Simplifying
(4y + -5x)(2y + 7x) = 0

Reorder the terms:
(-5x + 4y)(2y + 7x) = 0

Reorder the terms:
(-5x + 4y)(7x + 2y) = 0

Multiply (-5x + 4y) * (7x + 2y)
(-5x * (7x + 2y) + 4y * (7x + 2y)) = 0
((7x * -5x + 2y * -5x) + 4y * (7x + 2y)) = 0

Reorder the terms:
((-10xy + -35x2) + 4y * (7x + 2y)) = 0
((-10xy + -35x2) + 4y * (7x + 2y)) = 0
(-10xy + -35x2 + (7x * 4y + 2y * 4y)) = 0
(-10xy + -35x2 + (28xy + 8y2)) = 0

Reorder the terms:
(-10xy + 28xy + -35x2 + 8y2) = 0

Combine like terms: -10xy + 28xy = 18xy
(18xy + -35x2 + 8y2) = 0

Solving
18xy + -35x2 + 8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7x + -2y)(5x + -4y) = 0


Subproblem 1
Set the factor '(-7x + -2y)' equal to zero and attempt to solve:

Simplifying
-7x + -2y = 0

Solving
-7x + -2y = 0

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

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

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

Divide each side by '-7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y

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 = {-0.2857142857y, 0.8y}

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