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

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Solution for (5x+4y)(x-7y)=0 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.
(x + -7y)(5x + 4y) = 0


Subproblem 1
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

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 = {7y, -0.8y}

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