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

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


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

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

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

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

Combine like terms: 4xy + 35xy = 39xy
(39xy + 5x2 + 28y2) = 0

Solving
39xy + 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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