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

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


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

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

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

Reorder the terms:
4(-2xy + 6xy + 3x2 + -4y2) = 0

Combine like terms: -2xy + 6xy = 4xy
4(4xy + 3x2 + -4y2) = 0
(4xy * 4 + 3x2 * 4 + -4y2 * 4) = 0
(16xy + 12x2 + -16y2) = 0

Solving
16xy + 12x2 + -16y2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 4.

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 '(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
Solution
x = {0.6666666667y, -2y}

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