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

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


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

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

Reorder the terms:
0 = 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))

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

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

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

Solving
0 = 189xy2 + 504x2y + 147x3

Solving for variable 'x'.
Remove the zero:
-189xy2 + -504x2y + -147x3 = 189xy2 + 504x2y + 147x3 + -189xy2 + -504x2y + -147x3

Reorder the terms:
-189xy2 + -504x2y + -147x3 = 189xy2 + -189xy2 + 504x2y + -504x2y + 147x3 + -147x3

Combine like terms: 189xy2 + -189xy2 = 0
-189xy2 + -504x2y + -147x3 = 0 + 504x2y + -504x2y + 147x3 + -147x3
-189xy2 + -504x2y + -147x3 = 504x2y + -504x2y + 147x3 + -147x3

Combine like terms: 504x2y + -504x2y = 0
-189xy2 + -504x2y + -147x3 = 0 + 147x3 + -147x3
-189xy2 + -504x2y + -147x3 = 147x3 + -147x3

Combine like terms: 147x3 + -147x3 = 0
-189xy2 + -504x2y + -147x3 = 0

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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