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

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


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

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

Reorder the terms:
((-15xy + -6x2) + 4y * (2x + 5y)) = 0
((-15xy + -6x2) + 4y * (2x + 5y)) = 0
(-15xy + -6x2 + (2x * 4y + 5y * 4y)) = 0
(-15xy + -6x2 + (8xy + 20y2)) = 0

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

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

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

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2.5y, 1.333333333y}

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