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

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


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

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

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

Reorder the terms:
x((-12xy + 8x2) + -5y * (2x + -3y)) = 0
x((-12xy + 8x2) + -5y * (2x + -3y)) = 0
x(-12xy + 8x2 + (2x * -5y + -3y * -5y)) = 0
x(-12xy + 8x2 + (-10xy + 15y2)) = 0

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

Combine like terms: -12xy + -10xy = -22xy
x(-22xy + 8x2 + 15y2) = 0
(-22xy * x + 8x2 * x + 15y2 * x) = 0

Reorder the terms:
(15xy2 + -22x2y + 8x3) = 0
(15xy2 + -22x2y + 8x3) = 0

Solving
15xy2 + -22x2y + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15y2 + -22xy + 8x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5y + -4x)' equal to zero and attempt to solve:

Simplifying
5y + -4x = 0

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

Simplifying
3y + -2x = 0

Reorder the terms:
-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, 1.25y, 1.5y}

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