(3x+5y)(2x-4y)=

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Solution for (3x+5y)(2x-4y)= equation: 


Simplifying
(3x + 5y)(2x + -4y) = 0

Multiply (3x + 5y) * (2x + -4y)
(3x * (2x + -4y) + 5y * (2x + -4y)) = 0
((2x * 3x + -4y * 3x) + 5y * (2x + -4y)) = 0

Reorder the terms:
((-12xy + 6x2) + 5y * (2x + -4y)) = 0
((-12xy + 6x2) + 5y * (2x + -4y)) = 0
(-12xy + 6x2 + (2x * 5y + -4y * 5y)) = 0
(-12xy + 6x2 + (10xy + -20y2)) = 0

Reorder the terms:
(-12xy + 10xy + 6x2 + -20y2) = 0

Combine like terms: -12xy + 10xy = -2xy
(-2xy + 6x2 + -20y2) = 0

Solving
-2xy + 6x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1xy + 3x2 + -10y2) = 0

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

Ignore the factor 2.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

Subproblem 2
Set the factor '(3x + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {2y, -1.666666667y}

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