2(2x-3y)(2x+5y)=

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Solution for 2(2x-3y)(2x+5y)= equation: 


Simplifying
2(2x + -3y)(2x + 5y) = 0

Multiply (2x + -3y) * (2x + 5y)
2(2x * (2x + 5y) + -3y * (2x + 5y)) = 0
2((2x * 2x + 5y * 2x) + -3y * (2x + 5y)) = 0

Reorder the terms:
2((10xy + 4x2) + -3y * (2x + 5y)) = 0
2((10xy + 4x2) + -3y * (2x + 5y)) = 0
2(10xy + 4x2 + (2x * -3y + 5y * -3y)) = 0
2(10xy + 4x2 + (-6xy + -15y2)) = 0

Reorder the terms:
2(10xy + -6xy + 4x2 + -15y2) = 0

Combine like terms: 10xy + -6xy = 4xy
2(4xy + 4x2 + -15y2) = 0
(4xy * 2 + 4x2 * 2 + -15y2 * 2) = 0
(8xy + 8x2 + -30y2) = 0

Solving
8xy + 8x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4xy + 4x2 + -15y2) = 0

Factor a trinomial.
2((2x + -3y)(2x + 5y)) = 0

Ignore the factor 2.

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 '(2x + 5y)' equal to zero and attempt to solve:

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {1.5y, -2.5y}

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