2X-6-(X-3)(2X-5)=(X-3)(7-2X)

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Solution for 2X-6-(X-3)(2X-5)=(X-3)(7-2X) equation: 


Simplifying
2X + -6 + -1(X + -3)(2X + -5) = (X + -3)(7 + -2X)

Reorder the terms:
2X + -6 + -1(-3 + X)(2X + -5) = (X + -3)(7 + -2X)

Reorder the terms:
2X + -6 + -1(-3 + X)(-5 + 2X) = (X + -3)(7 + -2X)

Multiply (-3 + X) * (-5 + 2X)
2X + -6 + -1(-3(-5 + 2X) + X(-5 + 2X)) = (X + -3)(7 + -2X)
2X + -6 + -1((-5 * -3 + 2X * -3) + X(-5 + 2X)) = (X + -3)(7 + -2X)
2X + -6 + -1((15 + -6X) + X(-5 + 2X)) = (X + -3)(7 + -2X)
2X + -6 + -1(15 + -6X + (-5 * X + 2X * X)) = (X + -3)(7 + -2X)
2X + -6 + -1(15 + -6X + (-5X + 2X2)) = (X + -3)(7 + -2X)

Combine like terms: -6X + -5X = -11X
2X + -6 + -1(15 + -11X + 2X2) = (X + -3)(7 + -2X)
2X + -6 + (15 * -1 + -11X * -1 + 2X2 * -1) = (X + -3)(7 + -2X)
2X + -6 + (-15 + 11X + -2X2) = (X + -3)(7 + -2X)

Reorder the terms:
-6 + -15 + 2X + 11X + -2X2 = (X + -3)(7 + -2X)

Combine like terms: -6 + -15 = -21
-21 + 2X + 11X + -2X2 = (X + -3)(7 + -2X)

Combine like terms: 2X + 11X = 13X
-21 + 13X + -2X2 = (X + -3)(7 + -2X)

Reorder the terms:
-21 + 13X + -2X2 = (-3 + X)(7 + -2X)

Multiply (-3 + X) * (7 + -2X)
-21 + 13X + -2X2 = (-3(7 + -2X) + X(7 + -2X))
-21 + 13X + -2X2 = ((7 * -3 + -2X * -3) + X(7 + -2X))
-21 + 13X + -2X2 = ((-21 + 6X) + X(7 + -2X))
-21 + 13X + -2X2 = (-21 + 6X + (7 * X + -2X * X))
-21 + 13X + -2X2 = (-21 + 6X + (7X + -2X2))

Combine like terms: 6X + 7X = 13X
-21 + 13X + -2X2 = (-21 + 13X + -2X2)

Add '21' to each side of the equation.
-21 + 13X + 21 + -2X2 = -21 + 13X + 21 + -2X2

Reorder the terms:
-21 + 21 + 13X + -2X2 = -21 + 13X + 21 + -2X2

Combine like terms: -21 + 21 = 0
0 + 13X + -2X2 = -21 + 13X + 21 + -2X2
13X + -2X2 = -21 + 13X + 21 + -2X2

Reorder the terms:
13X + -2X2 = -21 + 21 + 13X + -2X2

Combine like terms: -21 + 21 = 0
13X + -2X2 = 0 + 13X + -2X2
13X + -2X2 = 13X + -2X2

Add '-13X' to each side of the equation.
13X + -13X + -2X2 = 13X + -13X + -2X2

Combine like terms: 13X + -13X = 0
0 + -2X2 = 13X + -13X + -2X2
-2X2 = 13X + -13X + -2X2

Combine like terms: 13X + -13X = 0
-2X2 = 0 + -2X2
-2X2 = -2X2

Add '2X2' to each side of the equation.
-2X2 + 2X2 = -2X2 + 2X2

Combine like terms: -2X2 + 2X2 = 0
0 = -2X2 + 2X2

Combine like terms: -2X2 + 2X2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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