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

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

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

Reorder the terms:
(-2xy + x2) + -5y(3x + -6y) = 0
(-2xy + x2) + -5y(3x + -6y) = 0
-2xy + x2 + (3x * -5y + -6y * -5y) = 0
-2xy + x2 + (-15xy + 30y2) = 0

Reorder the terms:
-2xy + -15xy + x2 + 30y2 = 0

Combine like terms: -2xy + -15xy = -17xy
-17xy + x2 + 30y2 = 0

Solving
-17xy + x2 + 30y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -15y)(x + -2y) = 0

Subproblem 1
Set the factor '(x + -15y)' equal to zero and attempt to solve:

Simplifying
x + -15y = 0

Solving
x + -15y = 0

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

Add '15y' to each side of the equation.
x + -15y + 15y = 0 + 15y

Combine like terms: -15y + 15y = 0
x + 0 = 0 + 15y
x = 0 + 15y
Remove the zero:
x = 15y

Simplifying
x = 15y
Subproblem 2
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
Solution
x = {15y, 2y}