T(x)=3xy-2x^2

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Solution for T(x)=3xy-2x^2 equation: 


Simplifying
T(x) = 3xy + -2x2

Multiply T * x
xT = 3xy + -2x2

Solving
xT = 3xy + -2x2

Solving for variable 'x'.

Reorder the terms:
xT + -3xy + 2x2 = 3xy + -3xy + -2x2 + 2x2

Combine like terms: 3xy + -3xy = 0
xT + -3xy + 2x2 = 0 + -2x2 + 2x2
xT + -3xy + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
xT + -3xy + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(T + -3y + 2x) = 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 '(T + -3y + 2x)' equal to zero and attempt to solve:

Simplifying
T + -3y + 2x = 0

Reorder the terms:
T + 2x + -3y = 0

Solving
T + 2x + -3y = 0

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

Add '-1T' to each side of the equation.
T + 2x + -1T + -3y = 0 + -1T

Reorder the terms:
T + -1T + 2x + -3y = 0 + -1T

Combine like terms: T + -1T = 0
0 + 2x + -3y = 0 + -1T
2x + -3y = 0 + -1T
Remove the zero:
2x + -3y = -1T

Add '3y' to each side of the equation.
2x + -3y + 3y = -1T + 3y

Combine like terms: -3y + 3y = 0
2x + 0 = -1T + 3y
2x = -1T + 3y

Divide each side by '2'.
x = -0.5T + 1.5y

Simplifying
x = -0.5T + 1.5y
Solution
x = {0, -0.5T + 1.5y}

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