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

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Solution for (x+y)(6x-8y)=0 equation: 


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

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

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

Reorder the terms:
(-8xy + 6xy + 6x2 + -8y2) = 0

Combine like terms: -8xy + 6xy = -2xy
(-2xy + 6x2 + -8y2) = 0

Solving
-2xy + 6x2 + -8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1xy + 3x2 + -4y2) = 0

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

Ignore the factor 2.

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

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

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

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

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {1.333333333y, -1y}

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