(6x+6y)(x-5y)=

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


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

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

Reorder the terms:
((-30xy + 6x2) + 6y * (x + -5y)) = 0
((-30xy + 6x2) + 6y * (x + -5y)) = 0
(-30xy + 6x2 + (x * 6y + -5y * 6y)) = 0
(-30xy + 6x2 + (6xy + -30y2)) = 0

Reorder the terms:
(-30xy + 6xy + 6x2 + -30y2) = 0

Combine like terms: -30xy + 6xy = -24xy
(-24xy + 6x2 + -30y2) = 0

Solving
-24xy + 6x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4xy + x2 + -5y2) = 0

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

Ignore the factor 6.

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

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

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

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

Simplifying
x = 5y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {5y, -1y}

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