=8x^2-2xy-3y^2

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Solution for =8x^2-2xy-3y^2 equation: 


Simplifying
0 = 8x2 + -2xy + -3y2

Reorder the terms:
0 = -2xy + 8x2 + -3y2

Solving
0 = -2xy + 8x2 + -3y2

Solving for variable 'x'.
Remove the zero:
2xy + -8x2 + 3y2 = -2xy + 8x2 + -3y2 + 2xy + -8x2 + 3y2

Reorder the terms:
2xy + -8x2 + 3y2 = -2xy + 2xy + 8x2 + -8x2 + -3y2 + 3y2

Combine like terms: -2xy + 2xy = 0
2xy + -8x2 + 3y2 = 0 + 8x2 + -8x2 + -3y2 + 3y2
2xy + -8x2 + 3y2 = 8x2 + -8x2 + -3y2 + 3y2

Combine like terms: 8x2 + -8x2 = 0
2xy + -8x2 + 3y2 = 0 + -3y2 + 3y2
2xy + -8x2 + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
2xy + -8x2 + 3y2 = 0

Factor a trinomial.
(-2x + -1y)(4x + -3y) = 0


Subproblem 1
Set the factor '(-2x + -1y)' equal to zero and attempt to solve:

Simplifying
-2x + -1y = 0

Solving
-2x + -1y = 0

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

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

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

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

Simplifying
x = -0.5y

Subproblem 2
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
Solution
x = {-0.5y, 0.75y}

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