(7x+8y)(8x-6y)=

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Solution for (7x+8y)(8x-6y)= equation: 


Simplifying
(7x + 8y)(8x + -6y) = 0

Multiply (7x + 8y) * (8x + -6y)
(7x * (8x + -6y) + 8y * (8x + -6y)) = 0
((8x * 7x + -6y * 7x) + 8y * (8x + -6y)) = 0

Reorder the terms:
((-42xy + 56x2) + 8y * (8x + -6y)) = 0
((-42xy + 56x2) + 8y * (8x + -6y)) = 0
(-42xy + 56x2 + (8x * 8y + -6y * 8y)) = 0
(-42xy + 56x2 + (64xy + -48y2)) = 0

Reorder the terms:
(-42xy + 64xy + 56x2 + -48y2) = 0

Combine like terms: -42xy + 64xy = 22xy
(22xy + 56x2 + -48y2) = 0

Solving
22xy + 56x2 + -48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11xy + 28x2 + -24y2) = 0

Factor a trinomial.
2((4x + -3y)(7x + 8y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4x + -3y)' equal to zero and attempt to solve:

Simplifying
4x + -3y = 0

Solving
4x + -3y = 0

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

Add '3y' to each side of the equation.
4x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
4x + 0 = 0 + 3y
4x = 0 + 3y
Remove the zero:
4x = 3y

Divide each side by '4'.
x = 0.75y

Simplifying
x = 0.75y

Subproblem 2
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
Solution
x = {0.75y, -1.142857143y}

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