(4x-5y)(3x-y)=0

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Solution for (4x-5y)(3x-y)=0 equation: 


Simplifying
(4x + -5y)(3x + -1y) = 0

Multiply (4x + -5y) * (3x + -1y)
(4x * (3x + -1y) + -5y * (3x + -1y)) = 0
((3x * 4x + -1y * 4x) + -5y * (3x + -1y)) = 0

Reorder the terms:
((-4xy + 12x2) + -5y * (3x + -1y)) = 0
((-4xy + 12x2) + -5y * (3x + -1y)) = 0
(-4xy + 12x2 + (3x * -5y + -1y * -5y)) = 0
(-4xy + 12x2 + (-15xy + 5y2)) = 0

Reorder the terms:
(-4xy + -15xy + 12x2 + 5y2) = 0

Combine like terms: -4xy + -15xy = -19xy
(-19xy + 12x2 + 5y2) = 0

Solving
-19xy + 12x2 + 5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -5y)(3x + -1y) = 0


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

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

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

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

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y

Subproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {1.25y, 0.3333333333y}

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