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

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Solution for 6(4x+2y)(6x-5y)=0 equation: 


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

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

Reorder the terms:
6((-20xy + 24x2) + 2y * (6x + -5y)) = 0
6((-20xy + 24x2) + 2y * (6x + -5y)) = 0
6(-20xy + 24x2 + (6x * 2y + -5y * 2y)) = 0
6(-20xy + 24x2 + (12xy + -10y2)) = 0

Reorder the terms:
6(-20xy + 12xy + 24x2 + -10y2) = 0

Combine like terms: -20xy + 12xy = -8xy
6(-8xy + 24x2 + -10y2) = 0
(-8xy * 6 + 24x2 * 6 + -10y2 * 6) = 0
(-48xy + 144x2 + -60y2) = 0

Solving
-48xy + 144x2 + -60y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-4xy + 12x2 + -5y2) = 0

Factor a trinomial.
12((6x + -5y)(2x + y)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve:

Simplifying
6x + -5y = 0

Solving
6x + -5y = 0

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

Add '5y' to each side of the equation.
6x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
6x + 0 = 0 + 5y
6x = 0 + 5y
Remove the zero:
6x = 5y

Divide each side by '6'.
x = 0.8333333333y

Simplifying
x = 0.8333333333y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {0.8333333333y, -0.5y}

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