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

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


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

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

Reorder the terms:
((20xy + 35x2) + -4y * (7x + 4y)) = 0
((20xy + 35x2) + -4y * (7x + 4y)) = 0
(20xy + 35x2 + (7x * -4y + 4y * -4y)) = 0
(20xy + 35x2 + (-28xy + -16y2)) = 0

Reorder the terms:
(20xy + -28xy + 35x2 + -16y2) = 0

Combine like terms: 20xy + -28xy = -8xy
(-8xy + 35x2 + -16y2) = 0

Solving
-8xy + 35x2 + -16y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(7x + 4y)' equal to zero and attempt to solve:

Simplifying
7x + 4y = 0

Solving
7x + 4y = 0

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

Add '-4y' to each side of the equation.
7x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
7x + 0 = 0 + -4y
7x = 0 + -4y
Remove the zero:
7x = -4y

Divide each side by '7'.
x = -0.5714285714y

Simplifying
x = -0.5714285714y
Solution
x = {0.8y, -0.5714285714y}

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