(x+3y)(9x-y)=

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Solution for (x+3y)(9x-y)= equation: 


Simplifying
(x + 3y)(9x + -1y) = 0

Multiply (x + 3y) * (9x + -1y)
(x(9x + -1y) + 3y * (9x + -1y)) = 0
((9x * x + -1y * x) + 3y * (9x + -1y)) = 0

Reorder the terms:
((-1xy + 9x2) + 3y * (9x + -1y)) = 0
((-1xy + 9x2) + 3y * (9x + -1y)) = 0
(-1xy + 9x2 + (9x * 3y + -1y * 3y)) = 0
(-1xy + 9x2 + (27xy + -3y2)) = 0

Reorder the terms:
(-1xy + 27xy + 9x2 + -3y2) = 0

Combine like terms: -1xy + 27xy = 26xy
(26xy + 9x2 + -3y2) = 0

Solving
26xy + 9x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9x + -1y)(x + 3y) = 0


Subproblem 1
Set the factor '(9x + -1y)' equal to zero and attempt to solve:

Simplifying
9x + -1y = 0

Solving
9x + -1y = 0

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

Add 'y' to each side of the equation.
9x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
9x + 0 = 0 + y
9x = 0 + y
Remove the zero:
9x = y

Divide each side by '9'.
x = 0.1111111111y

Simplifying
x = 0.1111111111y

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

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {0.1111111111y, -3y}

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