(8x+4y)(7x-8y)=

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Solution for (8x+4y)(7x-8y)= equation: 


Simplifying
(8x + 4y)(7x + -8y) = 0

Multiply (8x + 4y) * (7x + -8y)
(8x * (7x + -8y) + 4y * (7x + -8y)) = 0
((7x * 8x + -8y * 8x) + 4y * (7x + -8y)) = 0

Reorder the terms:
((-64xy + 56x2) + 4y * (7x + -8y)) = 0
((-64xy + 56x2) + 4y * (7x + -8y)) = 0
(-64xy + 56x2 + (7x * 4y + -8y * 4y)) = 0
(-64xy + 56x2 + (28xy + -32y2)) = 0

Reorder the terms:
(-64xy + 28xy + 56x2 + -32y2) = 0

Combine like terms: -64xy + 28xy = -36xy
(-36xy + 56x2 + -32y2) = 0

Solving
-36xy + 56x2 + -32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9xy + 14x2 + -8y2) = 0

Factor a trinomial.
4((7x + -8y)(2x + y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7x + -8y)' equal to zero and attempt to solve:

Simplifying
7x + -8y = 0

Solving
7x + -8y = 0

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

Add '8y' to each side of the equation.
7x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
7x + 0 = 0 + 8y
7x = 0 + 8y
Remove the zero:
7x = 8y

Divide each side by '7'.
x = 1.142857143y

Simplifying
x = 1.142857143y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {1.142857143y, -0.5y}

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