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

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


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

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

Reorder the terms:
((-18xy + 15x2) + 5y * (5x + -6y)) = 0
((-18xy + 15x2) + 5y * (5x + -6y)) = 0
(-18xy + 15x2 + (5x * 5y + -6y * 5y)) = 0
(-18xy + 15x2 + (25xy + -30y2)) = 0

Reorder the terms:
(-18xy + 25xy + 15x2 + -30y2) = 0

Combine like terms: -18xy + 25xy = 7xy
(7xy + 15x2 + -30y2) = 0

Solving
7xy + 15x2 + -30y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -6y)(3x + 5y) = 0


Subproblem 1
Set the factor '(5x + -6y)' equal to zero and attempt to solve:

Simplifying
5x + -6y = 0

Solving
5x + -6y = 0

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

Add '6y' to each side of the equation.
5x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
5x + 0 = 0 + 6y
5x = 0 + 6y
Remove the zero:
5x = 6y

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y

Subproblem 2
Set the factor '(3x + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {1.2y, -1.666666667y}

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