(5x+12y)(2x+3y)=

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Solution for (5x+12y)(2x+3y)= equation: 


Simplifying
(5x + 12y)(2x + 3y) = 0

Multiply (5x + 12y) * (2x + 3y)
(5x * (2x + 3y) + 12y * (2x + 3y)) = 0
((2x * 5x + 3y * 5x) + 12y * (2x + 3y)) = 0

Reorder the terms:
((15xy + 10x2) + 12y * (2x + 3y)) = 0
((15xy + 10x2) + 12y * (2x + 3y)) = 0
(15xy + 10x2 + (2x * 12y + 3y * 12y)) = 0
(15xy + 10x2 + (24xy + 36y2)) = 0

Reorder the terms:
(15xy + 24xy + 10x2 + 36y2) = 0

Combine like terms: 15xy + 24xy = 39xy
(39xy + 10x2 + 36y2) = 0

Solving
39xy + 10x2 + 36y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + 3y)(5x + 12y) = 0


Subproblem 1
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 2
Set the factor '(5x + 12y)' equal to zero and attempt to solve:

Simplifying
5x + 12y = 0

Solving
5x + 12y = 0

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

Add '-12y' to each side of the equation.
5x + 12y + -12y = 0 + -12y

Combine like terms: 12y + -12y = 0
5x + 0 = 0 + -12y
5x = 0 + -12y
Remove the zero:
5x = -12y

Divide each side by '5'.
x = -2.4y

Simplifying
x = -2.4y
Solution
x = {-1.5y, -2.4y}

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