(3x-9y)(6x+7y)=

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Solution for (3x-9y)(6x+7y)= equation: 


Simplifying
(3x + -9y)(6x + 7y) = 0

Multiply (3x + -9y) * (6x + 7y)
(3x * (6x + 7y) + -9y * (6x + 7y)) = 0
((6x * 3x + 7y * 3x) + -9y * (6x + 7y)) = 0

Reorder the terms:
((21xy + 18x2) + -9y * (6x + 7y)) = 0
((21xy + 18x2) + -9y * (6x + 7y)) = 0
(21xy + 18x2 + (6x * -9y + 7y * -9y)) = 0
(21xy + 18x2 + (-54xy + -63y2)) = 0

Reorder the terms:
(21xy + -54xy + 18x2 + -63y2) = 0

Combine like terms: 21xy + -54xy = -33xy
(-33xy + 18x2 + -63y2) = 0

Solving
-33xy + 18x2 + -63y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-11xy + 6x2 + -21y2) = 0

Factor a trinomial.
3((x + -3y)(6x + 7y)) = 0

Ignore the factor 3.

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y

Subproblem 2
Set the factor '(6x + 7y)' equal to zero and attempt to solve:

Simplifying
6x + 7y = 0

Solving
6x + 7y = 0

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

Add '-7y' to each side of the equation.
6x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
6x + 0 = 0 + -7y
6x = 0 + -7y
Remove the zero:
6x = -7y

Divide each side by '6'.
x = -1.166666667y

Simplifying
x = -1.166666667y
Solution
x = {3y, -1.166666667y}

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