-2x[(5x-4y)-(3x+2y)+(2x+3y)]=

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


Simplifying
-2x[(5x + -4y) + -1(3x + 2y) + (2x + 3y)] = 0

Remove parenthesis around (5x + -4y)
-2x[5x + -4y + -1(3x + 2y) + (2x + 3y)] = 0
-2x[5x + -4y + (3x * -1 + 2y * -1) + (2x + 3y)] = 0
-2x[5x + -4y + (-3x + -2y) + (2x + 3y)] = 0

Remove parenthesis around (2x + 3y)
-2x[5x + -4y + -3x + -2y + 2x + 3y] = 0

Reorder the terms:
-2x[5x + -3x + 2x + -4y + -2y + 3y] = 0

Combine like terms: 5x + -3x = 2x
-2x[2x + 2x + -4y + -2y + 3y] = 0

Combine like terms: 2x + 2x = 4x
-2x[4x + -4y + -2y + 3y] = 0

Combine like terms: -4y + -2y = -6y
-2x[4x + -6y + 3y] = 0

Combine like terms: -6y + 3y = -3y
-2x[4x + -3y] = 0
[4x * -2x + -3y * -2x] = 0

Reorder the terms:
[6xy + -8x2] = 0
[6xy + -8x2] = 0

Solving
6xy + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3y + -4x) = 0

Ignore the factor 2.

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 '(3y + -4x)' equal to zero and attempt to solve:

Simplifying
3y + -4x = 0

Reorder the terms:
-4x + 3y = 0

Solving
-4x + 3y = 0

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

Add '-3y' to each side of the equation.
-4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-4x + 0 = 0 + -3y
-4x = 0 + -3y
Remove the zero:
-4x = -3y

Divide each side by '-4'.
x = 0.75y

Simplifying
x = 0.75y
Solution
x = {0, 0.75y}

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