(2x+5y)(3x+6y)=

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Solution for (2x+5y)(3x+6y)= equation: 


Simplifying
(2x + 5y)(3x + 6y) = 0

Multiply (2x + 5y) * (3x + 6y)
(2x * (3x + 6y) + 5y * (3x + 6y)) = 0
((3x * 2x + 6y * 2x) + 5y * (3x + 6y)) = 0

Reorder the terms:
((12xy + 6x2) + 5y * (3x + 6y)) = 0
((12xy + 6x2) + 5y * (3x + 6y)) = 0
(12xy + 6x2 + (3x * 5y + 6y * 5y)) = 0
(12xy + 6x2 + (15xy + 30y2)) = 0

Reorder the terms:
(12xy + 15xy + 6x2 + 30y2) = 0

Combine like terms: 12xy + 15xy = 27xy
(27xy + 6x2 + 30y2) = 0

Solving
27xy + 6x2 + 30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9xy + 2x2 + 10y2) = 0

Factor a trinomial.
3((x + 2y)(2x + 5y)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(2x + 5y)' equal to zero and attempt to solve:

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {-2y, -2.5y}

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