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

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


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

Reorder the terms:
(2x + 3y)(5x + -4y) = 0

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

Reorder the terms:
((-8xy + 10x2) + 3y * (5x + -4y)) = 0
((-8xy + 10x2) + 3y * (5x + -4y)) = 0
(-8xy + 10x2 + (5x * 3y + -4y * 3y)) = 0
(-8xy + 10x2 + (15xy + -12y2)) = 0

Reorder the terms:
(-8xy + 15xy + 10x2 + -12y2) = 0

Combine like terms: -8xy + 15xy = 7xy
(7xy + 10x2 + -12y2) = 0

Solving
7xy + 10x2 + -12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -4y)(2x + 3y) = 0


Subproblem 1
Set the factor '(5x + -4y)' equal to zero and attempt to solve:

Simplifying
5x + -4y = 0

Solving
5x + -4y = 0

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

Add '4y' to each side of the equation.
5x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
5x + 0 = 0 + 4y
5x = 0 + 4y
Remove the zero:
5x = 4y

Divide each side by '5'.
x = 0.8y

Simplifying
x = 0.8y

Subproblem 2
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
Solution
x = {0.8y, -1.5y}

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