(4x+5y)*(3x-6y)=0

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Solution for (4x+5y)*(3x-6y)=0 equation: 


Simplifying
(4x + 5y)(3x + -6y) = 0

Multiply (4x + 5y) * (3x + -6y)
(4x * (3x + -6y) + 5y * (3x + -6y)) = 0
((3x * 4x + -6y * 4x) + 5y * (3x + -6y)) = 0

Reorder the terms:
((-24xy + 12x2) + 5y * (3x + -6y)) = 0
((-24xy + 12x2) + 5y * (3x + -6y)) = 0
(-24xy + 12x2 + (3x * 5y + -6y * 5y)) = 0
(-24xy + 12x2 + (15xy + -30y2)) = 0

Reorder the terms:
(-24xy + 15xy + 12x2 + -30y2) = 0

Combine like terms: -24xy + 15xy = -9xy
(-9xy + 12x2 + -30y2) = 0

Solving
-9xy + 12x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3xy + 4x2 + -10y2) = 0

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

Ignore the factor 3.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

Subproblem 2
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
Solution
x = {2y, -1.25y}

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