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

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


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

Multiply y * x
xy = 3x(x + -6)

Reorder the terms:
xy = 3x(-6 + x)
xy = (-6 * 3x + x * 3x)
xy = (-18x + 3x2)

Solving
xy = -18x + 3x2

Solving for variable 'x'.

Reorder the terms:
18x + xy + -3x2 = -18x + 3x2 + 18x + -3x2

Reorder the terms:
18x + xy + -3x2 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
18x + xy + -3x2 = 0 + 3x2 + -3x2
18x + xy + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18x + xy + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(18 + 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 '(18 + y + -3x)' equal to zero and attempt to solve:

Simplifying
18 + y + -3x = 0

Reorder the terms:
18 + -3x + y = 0

Solving
18 + -3x + y = 0

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

Add '-18' to each side of the equation.
18 + -3x + -18 + y = 0 + -18

Reorder the terms:
18 + -18 + -3x + y = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -3x + y = 0 + -18
-3x + y = 0 + -18

Combine like terms: 0 + -18 = -18
-3x + y = -18

Add '-1y' to each side of the equation.
-3x + y + -1y = -18 + -1y

Combine like terms: y + -1y = 0
-3x + 0 = -18 + -1y
-3x = -18 + -1y

Divide each side by '-3'.
x = 6 + 0.3333333333y

Simplifying
x = 6 + 0.3333333333y
Solution
x = {0, 6 + 0.3333333333y}

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