x(3x-y)(4x+5y)=

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Solution for x(3x-y)(4x+5y)= equation: 


Simplifying
x(3x + -1y)(4x + 5y) = 0

Multiply (3x + -1y) * (4x + 5y)
x(3x * (4x + 5y) + -1y * (4x + 5y)) = 0
x((4x * 3x + 5y * 3x) + -1y * (4x + 5y)) = 0

Reorder the terms:
x((15xy + 12x2) + -1y * (4x + 5y)) = 0
x((15xy + 12x2) + -1y * (4x + 5y)) = 0
x(15xy + 12x2 + (4x * -1y + 5y * -1y)) = 0
x(15xy + 12x2 + (-4xy + -5y2)) = 0

Reorder the terms:
x(15xy + -4xy + 12x2 + -5y2) = 0

Combine like terms: 15xy + -4xy = 11xy
x(11xy + 12x2 + -5y2) = 0
(11xy * x + 12x2 * x + -5y2 * x) = 0

Reorder the terms:
(-5xy2 + 11x2y + 12x3) = 0
(-5xy2 + 11x2y + 12x3) = 0

Solving
-5xy2 + 11x2y + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5y2 + 11xy + 12x2) = 0

Factor a trinomial.
x((-5y + -4x)(y + -3x)) = 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 '(-5y + -4x)' equal to zero and attempt to solve:

Simplifying
-5y + -4x = 0

Reorder the terms:
-4x + -5y = 0

Solving
-4x + -5y = 0

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

Add '5y' to each side of the equation.
-4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-4x + 0 = 0 + 5y
-4x = 0 + 5y
Remove the zero:
-4x = 5y

Divide each side by '-4'.
x = -1.25y

Simplifying
x = -1.25y

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, -1.25y, 0.3333333333y}

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