7x(7x+3y)(3x+9y)=

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Solution for 7x(7x+3y)(3x+9y)= equation: 


Simplifying
7x(7x + 3y)(3x + 9y) = 0

Multiply (7x + 3y) * (3x + 9y)
7x(7x * (3x + 9y) + 3y * (3x + 9y)) = 0
7x((3x * 7x + 9y * 7x) + 3y * (3x + 9y)) = 0

Reorder the terms:
7x((63xy + 21x2) + 3y * (3x + 9y)) = 0
7x((63xy + 21x2) + 3y * (3x + 9y)) = 0
7x(63xy + 21x2 + (3x * 3y + 9y * 3y)) = 0
7x(63xy + 21x2 + (9xy + 27y2)) = 0

Reorder the terms:
7x(63xy + 9xy + 21x2 + 27y2) = 0

Combine like terms: 63xy + 9xy = 72xy
7x(72xy + 21x2 + 27y2) = 0
(72xy * 7x + 21x2 * 7x + 27y2 * 7x) = 0

Reorder the terms:
(189xy2 + 504x2y + 147x3) = 0
(189xy2 + 504x2y + 147x3) = 0

Solving
189xy2 + 504x2y + 147x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '21x'.
21x(9y2 + 24xy + 7x2) = 0

Factor a trinomial.
21x((3y + x)(3y + 7x)) = 0

Ignore the factor 21.

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

Simplifying
3y + x = 0

Reorder the terms:
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

Subproblem 3
Set the factor '(3y + 7x)' equal to zero and attempt to solve:

Simplifying
3y + 7x = 0

Reorder the terms:
7x + 3y = 0

Solving
7x + 3y = 0

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

Add '-3y' to each side of the equation.
7x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
7x + 0 = 0 + -3y
7x = 0 + -3y
Remove the zero:
7x = -3y

Divide each side by '7'.
x = -0.4285714286y

Simplifying
x = -0.4285714286y
Solution
x = {0, -3y, -0.4285714286y}

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