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

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


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

Reorder the terms for easier multiplication:
x(2x + -3y)(5x + y) = 0

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

Reorder the terms:
x((2xy + 10x2) + -3y * (5x + y)) = 0
x((2xy + 10x2) + -3y * (5x + y)) = 0
x(2xy + 10x2 + (5x * -3y + y * -3y)) = 0
x(2xy + 10x2 + (-15xy + -3y2)) = 0

Reorder the terms:
x(2xy + -15xy + 10x2 + -3y2) = 0

Combine like terms: 2xy + -15xy = -13xy
x(-13xy + 10x2 + -3y2) = 0
(-13xy * x + 10x2 * x + -3y2 * x) = 0

Reorder the terms:
(-3xy2 + -13x2y + 10x3) = 0
(-3xy2 + -13x2y + 10x3) = 0

Solving
-3xy2 + -13x2y + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3y2 + -13xy + 10x2) = 0

Factor a trinomial.
x((-1y + -5x)(3y + -2x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1y + -5x)' equal to zero and attempt to solve:

Simplifying
-1y + -5x = 0

Reorder the terms:
-5x + -1y = 0

Solving
-5x + -1y = 0

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

Add 'y' to each side of the equation.
-5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-5x + 0 = 0 + y
-5x = 0 + y
Remove the zero:
-5x = y

Divide each side by '-5'.
x = -0.2y

Simplifying
x = -0.2y

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

Simplifying
3y + -2x = 0

Reorder the terms:
-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
Solution
x = {0, -0.2y, 1.5y}

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