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

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


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

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

Reorder the terms:
((35xy + 5x2) + -4y * (x + 7y)) = 0
((35xy + 5x2) + -4y * (x + 7y)) = 0
(35xy + 5x2 + (x * -4y + 7y * -4y)) = 0
(35xy + 5x2 + (-4xy + -28y2)) = 0

Reorder the terms:
(35xy + -4xy + 5x2 + -28y2) = 0

Combine like terms: 35xy + -4xy = 31xy
(31xy + 5x2 + -28y2) = 0

Solving
31xy + 5x2 + -28y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -4y)(x + 7y) = 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 '(x + 7y)' equal to zero and attempt to solve:

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

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

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

Simplifying
x = -7y
Solution
x = {0.8y, -7y}

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