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

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


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

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

Reorder the terms:
((-8xy + 20x2) + 3y * (5x + -2y)) = 0
((-8xy + 20x2) + 3y * (5x + -2y)) = 0
(-8xy + 20x2 + (5x * 3y + -2y * 3y)) = 0
(-8xy + 20x2 + (15xy + -6y2)) = 0

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

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

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

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(5x + -2y)' equal to zero and attempt to solve:

Simplifying
5x + -2y = 0

Solving
5x + -2y = 0

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

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

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

Divide each side by '5'.
x = 0.4y

Simplifying
x = 0.4y

Subproblem 2
Set the factor '(4x + 3y)' equal to zero and attempt to solve:

Simplifying
4x + 3y = 0

Solving
4x + 3y = 0

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

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

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

Divide each side by '4'.
x = -0.75y

Simplifying
x = -0.75y
Solution
x = {0.4y, -0.75y}

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