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

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


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

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

Reorder the terms:
((-8xy + 6x2) + 5y * (3x + -4y)) = 0
((-8xy + 6x2) + 5y * (3x + -4y)) = 0
(-8xy + 6x2 + (3x * 5y + -4y * 5y)) = 0
(-8xy + 6x2 + (15xy + -20y2)) = 0

Reorder the terms:
(-8xy + 15xy + 6x2 + -20y2) = 0

Combine like terms: -8xy + 15xy = 7xy
(7xy + 6x2 + -20y2) = 0

Solving
7xy + 6x2 + -20y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

Add '4y' to each side of the equation.
3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
3x + 0 = 0 + 4y
3x = 0 + 4y
Remove the zero:
3x = 4y

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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 = {1.333333333y, -2.5y}

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