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

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


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

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

Reorder the terms:
2((-8xy + 6x2) + 3y * (3x + -4y)) = 0
2((-8xy + 6x2) + 3y * (3x + -4y)) = 0
2(-8xy + 6x2 + (3x * 3y + -4y * 3y)) = 0
2(-8xy + 6x2 + (9xy + -12y2)) = 0

Reorder the terms:
2(-8xy + 9xy + 6x2 + -12y2) = 0

Combine like terms: -8xy + 9xy = 1xy
2(1xy + 6x2 + -12y2) = 0
(1xy * 2 + 6x2 * 2 + -12y2 * 2) = 0
(2xy + 12x2 + -24y2) = 0

Solving
2xy + 12x2 + -24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + 6x2 + -12y2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

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

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

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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

Simplifying
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 = {1.333333333y, -1.5y}

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