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

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


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

Reorder the terms:
5x(-3x + 2y)(6x + 2y) = 0

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

Reorder the terms:
5x((-6xy + -18x2) + 2y * (6x + 2y)) = 0
5x((-6xy + -18x2) + 2y * (6x + 2y)) = 0
5x(-6xy + -18x2 + (6x * 2y + 2y * 2y)) = 0
5x(-6xy + -18x2 + (12xy + 4y2)) = 0

Reorder the terms:
5x(-6xy + 12xy + -18x2 + 4y2) = 0

Combine like terms: -6xy + 12xy = 6xy
5x(6xy + -18x2 + 4y2) = 0
(6xy * 5x + -18x2 * 5x + 4y2 * 5x) = 0

Reorder the terms:
(20xy2 + 30x2y + -90x3) = 0
(20xy2 + 30x2y + -90x3) = 0

Solving
20xy2 + 30x2y + -90x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
10x((2y + -3x)(y + 3x)) = 0

Ignore the factor 10.

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

Simplifying
2y + -3x = 0

Reorder the terms:
-3x + 2y = 0

Solving
-3x + 2y = 0

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

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

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

Divide each side by '-3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

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

Simplifying
y + 3x = 0

Reorder the terms:
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {0, 0.6666666667y, -0.3333333333y}

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