(X+5)(x-7)=(2x+1)(X-7)

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Solution for (X+5)(x-7)=(2x+1)(X-7) equation:


Simplifying
(X + 5)(x + -7) = (2x + 1)(X + -7)

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

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

Multiply (5 + X) * (-7 + x)
(5(-7 + x) + X(-7 + x)) = (2x + 1)(X + -7)
((-7 * 5 + x * 5) + X(-7 + x)) = (2x + 1)(X + -7)
((-35 + 5x) + X(-7 + x)) = (2x + 1)(X + -7)
(-35 + 5x + (-7 * X + x * X)) = (2x + 1)(X + -7)
(-35 + 5x + (-7X + xX)) = (2x + 1)(X + -7)

Reorder the terms:
(-35 + -7X + 5x + xX) = (2x + 1)(X + -7)
(-35 + -7X + 5x + xX) = (2x + 1)(X + -7)

Reorder the terms:
-35 + -7X + 5x + xX = (1 + 2x)(X + -7)

Reorder the terms:
-35 + -7X + 5x + xX = (1 + 2x)(-7 + X)

Multiply (1 + 2x) * (-7 + X)
-35 + -7X + 5x + xX = (1(-7 + X) + 2x * (-7 + X))
-35 + -7X + 5x + xX = ((-7 * 1 + X * 1) + 2x * (-7 + X))
-35 + -7X + 5x + xX = ((-7 + 1X) + 2x * (-7 + X))
-35 + -7X + 5x + xX = (-7 + 1X + (-7 * 2x + X * 2x))
-35 + -7X + 5x + xX = (-7 + 1X + (-14x + 2xX))
-35 + -7X + 5x + xX = (-7 + 1X + -14x + 2xX)

Solving
-35 + -7X + 5x + xX = -7 + 1X + -14x + 2xX

Solving for variable 'X'.

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

Add '-1X' to each side of the equation.
-35 + -7X + 5x + -1X + xX = -7 + 1X + -14x + -1X + 2xX

Reorder the terms:
-35 + -7X + -1X + 5x + xX = -7 + 1X + -14x + -1X + 2xX

Combine like terms: -7X + -1X = -8X
-35 + -8X + 5x + xX = -7 + 1X + -14x + -1X + 2xX

Reorder the terms:
-35 + -8X + 5x + xX = -7 + 1X + -1X + -14x + 2xX

Combine like terms: 1X + -1X = 0
-35 + -8X + 5x + xX = -7 + 0 + -14x + 2xX
-35 + -8X + 5x + xX = -7 + -14x + 2xX

Add '-2xX' to each side of the equation.
-35 + -8X + 5x + xX + -2xX = -7 + -14x + 2xX + -2xX

Combine like terms: xX + -2xX = -1xX
-35 + -8X + 5x + -1xX = -7 + -14x + 2xX + -2xX

Combine like terms: 2xX + -2xX = 0
-35 + -8X + 5x + -1xX = -7 + -14x + 0
-35 + -8X + 5x + -1xX = -7 + -14x

Add '35' to each side of the equation.
-35 + -8X + 5x + 35 + -1xX = -7 + 35 + -14x

Reorder the terms:
-35 + 35 + -8X + 5x + -1xX = -7 + 35 + -14x

Combine like terms: -35 + 35 = 0
0 + -8X + 5x + -1xX = -7 + 35 + -14x
-8X + 5x + -1xX = -7 + 35 + -14x

Combine like terms: -7 + 35 = 28
-8X + 5x + -1xX = 28 + -14x

Add '-5x' to each side of the equation.
-8X + 5x + -5x + -1xX = 28 + -14x + -5x

Combine like terms: 5x + -5x = 0
-8X + 0 + -1xX = 28 + -14x + -5x
-8X + -1xX = 28 + -14x + -5x

Combine like terms: -14x + -5x = -19x
-8X + -1xX = 28 + -19x

Reorder the terms:
-28 + -8X + 19x + -1xX = 28 + -19x + -28 + 19x

Reorder the terms:
-28 + -8X + 19x + -1xX = 28 + -28 + -19x + 19x

Combine like terms: 28 + -28 = 0
-28 + -8X + 19x + -1xX = 0 + -19x + 19x
-28 + -8X + 19x + -1xX = -19x + 19x

Combine like terms: -19x + 19x = 0
-28 + -8X + 19x + -1xX = 0

The solution to this equation could not be determined.

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