3x(3x-2y)-5x(6y-x)+6xy=

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Solution for 3x(3x-2y)-5x(6y-x)+6xy= equation: 


Simplifying
3x(3x + -2y) + -5x(6y + -1x) + 6xy = 0
(3x * 3x + -2y * 3x) + -5x(6y + -1x) + 6xy = 0

Reorder the terms:
(-6xy + 9x2) + -5x(6y + -1x) + 6xy = 0
(-6xy + 9x2) + -5x(6y + -1x) + 6xy = 0

Reorder the terms:
-6xy + 9x2 + -5x(-1x + 6y) + 6xy = 0
-6xy + 9x2 + (-1x * -5x + 6y * -5x) + 6xy = 0

Reorder the terms:
-6xy + 9x2 + (-30xy + 5x2) + 6xy = 0
-6xy + 9x2 + (-30xy + 5x2) + 6xy = 0

Reorder the terms:
-6xy + -30xy + 6xy + 9x2 + 5x2 = 0

Combine like terms: -6xy + -30xy = -36xy
-36xy + 6xy + 9x2 + 5x2 = 0

Combine like terms: -36xy + 6xy = -30xy
-30xy + 9x2 + 5x2 = 0

Combine like terms: 9x2 + 5x2 = 14x2
-30xy + 14x2 = 0

Solving
-30xy + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-15y + 7x) = 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 '(-15y + 7x)' equal to zero and attempt to solve:

Simplifying
-15y + 7x = 0

Reorder the terms:
7x + -15y = 0

Solving
7x + -15y = 0

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

Add '15y' to each side of the equation.
7x + -15y + 15y = 0 + 15y

Combine like terms: -15y + 15y = 0
7x + 0 = 0 + 15y
7x = 0 + 15y
Remove the zero:
7x = 15y

Divide each side by '7'.
x = 2.142857143y

Simplifying
x = 2.142857143y
Solution
x = {0, 2.142857143y}

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