(6x+2y)x(9x+7y)=

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Solution for (6x+2y)x(9x+7y)= equation: 


Simplifying
(6x + 2y) * x(9x + 7y) = 0

Reorder the terms for easier multiplication:
x(6x + 2y)(9x + 7y) = 0

Multiply (6x + 2y) * (9x + 7y)
x(6x * (9x + 7y) + 2y * (9x + 7y)) = 0
x((9x * 6x + 7y * 6x) + 2y * (9x + 7y)) = 0

Reorder the terms:
x((42xy + 54x2) + 2y * (9x + 7y)) = 0
x((42xy + 54x2) + 2y * (9x + 7y)) = 0
x(42xy + 54x2 + (9x * 2y + 7y * 2y)) = 0
x(42xy + 54x2 + (18xy + 14y2)) = 0

Reorder the terms:
x(42xy + 18xy + 54x2 + 14y2) = 0

Combine like terms: 42xy + 18xy = 60xy
x(60xy + 54x2 + 14y2) = 0
(60xy * x + 54x2 * x + 14y2 * x) = 0

Reorder the terms:
(14xy2 + 60x2y + 54x3) = 0
(14xy2 + 60x2y + 54x3) = 0

Solving
14xy2 + 60x2y + 54x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7y2 + 30xy + 27x2) = 0

Factor a trinomial.
2x((7y + 9x)(y + 3x)) = 0

Ignore the factor 2.

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 '(7y + 9x)' equal to zero and attempt to solve:

Simplifying
7y + 9x = 0

Reorder the terms:
9x + 7y = 0

Solving
9x + 7y = 0

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

Add '-7y' to each side of the equation.
9x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
9x + 0 = 0 + -7y
9x = 0 + -7y
Remove the zero:
9x = -7y

Divide each side by '9'.
x = -0.7777777778y

Simplifying
x = -0.7777777778y

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, -0.7777777778y, -0.3333333333y}

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