-4(3x+2y)6(-2x-5y)=

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Solution for -4(3x+2y)6(-2x-5y)= equation: 


Simplifying
-4(3x + 2y) * 6(-2x + -5y) = 0

Reorder the terms for easier multiplication:
-4 * 6(3x + 2y)(-2x + -5y) = 0

Multiply -4 * 6
-24(3x + 2y)(-2x + -5y) = 0

Multiply (3x + 2y) * (-2x + -5y)
-24(3x * (-2x + -5y) + 2y * (-2x + -5y)) = 0
-24((-2x * 3x + -5y * 3x) + 2y * (-2x + -5y)) = 0

Reorder the terms:
-24((-15xy + -6x2) + 2y * (-2x + -5y)) = 0
-24((-15xy + -6x2) + 2y * (-2x + -5y)) = 0
-24(-15xy + -6x2 + (-2x * 2y + -5y * 2y)) = 0
-24(-15xy + -6x2 + (-4xy + -10y2)) = 0

Reorder the terms:
-24(-15xy + -4xy + -6x2 + -10y2) = 0

Combine like terms: -15xy + -4xy = -19xy
-24(-19xy + -6x2 + -10y2) = 0
(-19xy * -24 + -6x2 * -24 + -10y2 * -24) = 0
(456xy + 144x2 + 240y2) = 0

Solving
456xy + 144x2 + 240y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(19xy + 6x2 + 10y2) = 0

Factor a trinomial.
24((3x + 2y)(2x + 5y)) = 0

Ignore the factor 24.

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
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
Solution
x = {-0.6666666667y, -2.5y}

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