(x+6y)(3x-3y)=

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Solution for (x+6y)(3x-3y)= equation: 


Simplifying
(x + 6y)(3x + -3y) = 0

Multiply (x + 6y) * (3x + -3y)
(x(3x + -3y) + 6y * (3x + -3y)) = 0
((3x * x + -3y * x) + 6y * (3x + -3y)) = 0

Reorder the terms:
((-3xy + 3x2) + 6y * (3x + -3y)) = 0
((-3xy + 3x2) + 6y * (3x + -3y)) = 0
(-3xy + 3x2 + (3x * 6y + -3y * 6y)) = 0
(-3xy + 3x2 + (18xy + -18y2)) = 0

Reorder the terms:
(-3xy + 18xy + 3x2 + -18y2) = 0

Combine like terms: -3xy + 18xy = 15xy
(15xy + 3x2 + -18y2) = 0

Solving
15xy + 3x2 + -18y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5xy + x2 + -6y2) = 0

Factor a trinomial.
3((x + -1y)(x + 6y)) = 0

Ignore the factor 3.

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

Subproblem 2
Set the factor '(x + 6y)' equal to zero and attempt to solve:

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

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

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

Simplifying
x = -6y
Solution
x = {y, -6y}

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