2(2x-3y)(2x+8y)=0

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Solution for 2(2x-3y)(2x+8y)=0 equation: 


Simplifying
2(2x + -3y)(2x + 8y) = 0

Multiply (2x + -3y) * (2x + 8y)
2(2x * (2x + 8y) + -3y * (2x + 8y)) = 0
2((2x * 2x + 8y * 2x) + -3y * (2x + 8y)) = 0

Reorder the terms:
2((16xy + 4x2) + -3y * (2x + 8y)) = 0
2((16xy + 4x2) + -3y * (2x + 8y)) = 0
2(16xy + 4x2 + (2x * -3y + 8y * -3y)) = 0
2(16xy + 4x2 + (-6xy + -24y2)) = 0

Reorder the terms:
2(16xy + -6xy + 4x2 + -24y2) = 0

Combine like terms: 16xy + -6xy = 10xy
2(10xy + 4x2 + -24y2) = 0
(10xy * 2 + 4x2 * 2 + -24y2 * 2) = 0
(20xy + 8x2 + -48y2) = 0

Solving
20xy + 8x2 + -48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5xy + 2x2 + -12y2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(2x + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

Add '3y' to each side of the equation.
2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
2x + 0 = 0 + 3y
2x = 0 + 3y
Remove the zero:
2x = 3y

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y

Subproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {1.5y, -4y}

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