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

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


Simplifying
(4x + 7y)(5x + -1y) = 0

Multiply (4x + 7y) * (5x + -1y)
(4x * (5x + -1y) + 7y * (5x + -1y)) = 0
((5x * 4x + -1y * 4x) + 7y * (5x + -1y)) = 0

Reorder the terms:
((-4xy + 20x2) + 7y * (5x + -1y)) = 0
((-4xy + 20x2) + 7y * (5x + -1y)) = 0
(-4xy + 20x2 + (5x * 7y + -1y * 7y)) = 0
(-4xy + 20x2 + (35xy + -7y2)) = 0

Reorder the terms:
(-4xy + 35xy + 20x2 + -7y2) = 0

Combine like terms: -4xy + 35xy = 31xy
(31xy + 20x2 + -7y2) = 0

Solving
31xy + 20x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -1y)(4x + 7y) = 0


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

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y

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

Simplifying
4x + 7y = 0

Solving
4x + 7y = 0

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

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

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

Divide each side by '4'.
x = -1.75y

Simplifying
x = -1.75y
Solution
x = {0.2y, -1.75y}

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