3x(4x-5y)-4x(5y-x)+6xy=

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Solution for 3x(4x-5y)-4x(5y-x)+6xy= equation: 


Simplifying
3x(4x + -5y) + -4x(5y + -1x) + 6xy = 0
(4x * 3x + -5y * 3x) + -4x(5y + -1x) + 6xy = 0

Reorder the terms:
(-15xy + 12x2) + -4x(5y + -1x) + 6xy = 0
(-15xy + 12x2) + -4x(5y + -1x) + 6xy = 0

Reorder the terms:
-15xy + 12x2 + -4x(-1x + 5y) + 6xy = 0
-15xy + 12x2 + (-1x * -4x + 5y * -4x) + 6xy = 0

Reorder the terms:
-15xy + 12x2 + (-20xy + 4x2) + 6xy = 0
-15xy + 12x2 + (-20xy + 4x2) + 6xy = 0

Reorder the terms:
-15xy + -20xy + 6xy + 12x2 + 4x2 = 0

Combine like terms: -15xy + -20xy = -35xy
-35xy + 6xy + 12x2 + 4x2 = 0

Combine like terms: -35xy + 6xy = -29xy
-29xy + 12x2 + 4x2 = 0

Combine like terms: 12x2 + 4x2 = 16x2
-29xy + 16x2 = 0

Solving
-29xy + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-29y + 16x) = 0


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 '(-29y + 16x)' equal to zero and attempt to solve:

Simplifying
-29y + 16x = 0

Reorder the terms:
16x + -29y = 0

Solving
16x + -29y = 0

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

Add '29y' to each side of the equation.
16x + -29y + 29y = 0 + 29y

Combine like terms: -29y + 29y = 0
16x + 0 = 0 + 29y
16x = 0 + 29y
Remove the zero:
16x = 29y

Divide each side by '16'.
x = 1.8125y

Simplifying
x = 1.8125y
Solution
x = {0, 1.8125y}

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