5x(-3x+2y-4)-4x(3x-6y-10)=

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Solution for 5x(-3x+2y-4)-4x(3x-6y-10)= equation: 


Simplifying
5x(-3x + 2y + -4) + -4x(3x + -6y + -10) = 0

Reorder the terms:
5x(-4 + -3x + 2y) + -4x(3x + -6y + -10) = 0
(-4 * 5x + -3x * 5x + 2y * 5x) + -4x(3x + -6y + -10) = 0

Reorder the terms:
(-20x + 10xy + -15x2) + -4x(3x + -6y + -10) = 0
(-20x + 10xy + -15x2) + -4x(3x + -6y + -10) = 0

Reorder the terms:
-20x + 10xy + -15x2 + -4x(-10 + 3x + -6y) = 0
-20x + 10xy + -15x2 + (-10 * -4x + 3x * -4x + -6y * -4x) = 0

Reorder the terms:
-20x + 10xy + -15x2 + (40x + 24xy + -12x2) = 0
-20x + 10xy + -15x2 + (40x + 24xy + -12x2) = 0

Reorder the terms:
-20x + 40x + 10xy + 24xy + -15x2 + -12x2 = 0

Combine like terms: -20x + 40x = 20x
20x + 10xy + 24xy + -15x2 + -12x2 = 0

Combine like terms: 10xy + 24xy = 34xy
20x + 34xy + -15x2 + -12x2 = 0

Combine like terms: -15x2 + -12x2 = -27x2
20x + 34xy + -27x2 = 0

Solving
20x + 34xy + -27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + 34y + -27x) = 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 '(20 + 34y + -27x)' equal to zero and attempt to solve:

Simplifying
20 + 34y + -27x = 0

Reorder the terms:
20 + -27x + 34y = 0

Solving
20 + -27x + 34y = 0

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

Add '-20' to each side of the equation.
20 + -27x + -20 + 34y = 0 + -20

Reorder the terms:
20 + -20 + -27x + 34y = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -27x + 34y = 0 + -20
-27x + 34y = 0 + -20

Combine like terms: 0 + -20 = -20
-27x + 34y = -20

Add '-34y' to each side of the equation.
-27x + 34y + -34y = -20 + -34y

Combine like terms: 34y + -34y = 0
-27x + 0 = -20 + -34y
-27x = -20 + -34y

Divide each side by '-27'.
x = 0.7407407407 + 1.259259259y

Simplifying
x = 0.7407407407 + 1.259259259y
Solution
x = {0, 0.7407407407 + 1.259259259y}

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