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

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Solution for (6x-7)(X+5)=(2x+1)(3x+1) equation: 


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

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

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

Multiply (-7 + 6x) * (5 + X)
(-7(5 + X) + 6x * (5 + X)) = (2x + 1)(3x + 1)
((5 * -7 + X * -7) + 6x * (5 + X)) = (2x + 1)(3x + 1)
((-35 + -7X) + 6x * (5 + X)) = (2x + 1)(3x + 1)
(-35 + -7X + (5 * 6x + X * 6x)) = (2x + 1)(3x + 1)
(-35 + -7X + (30x + 6xX)) = (2x + 1)(3x + 1)
(-35 + -7X + 30x + 6xX) = (2x + 1)(3x + 1)

Reorder the terms:
-35 + -7X + 30x + 6xX = (1 + 2x)(3x + 1)

Reorder the terms:
-35 + -7X + 30x + 6xX = (1 + 2x)(1 + 3x)

Multiply (1 + 2x) * (1 + 3x)
-35 + -7X + 30x + 6xX = (1(1 + 3x) + 2x * (1 + 3x))
-35 + -7X + 30x + 6xX = ((1 * 1 + 3x * 1) + 2x * (1 + 3x))
-35 + -7X + 30x + 6xX = ((1 + 3x) + 2x * (1 + 3x))
-35 + -7X + 30x + 6xX = (1 + 3x + (1 * 2x + 3x * 2x))
-35 + -7X + 30x + 6xX = (1 + 3x + (2x + 6x2))

Combine like terms: 3x + 2x = 5x
-35 + -7X + 30x + 6xX = (1 + 5x + 6x2)

Solving
-35 + -7X + 30x + 6xX = 1 + 5x + 6x2

Solving for variable 'X'.

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

Add '35' to each side of the equation.
-35 + -7X + 30x + 35 + 6xX = 1 + 5x + 35 + 6x2

Reorder the terms:
-35 + 35 + -7X + 30x + 6xX = 1 + 5x + 35 + 6x2

Combine like terms: -35 + 35 = 0
0 + -7X + 30x + 6xX = 1 + 5x + 35 + 6x2
-7X + 30x + 6xX = 1 + 5x + 35 + 6x2

Reorder the terms:
-7X + 30x + 6xX = 1 + 35 + 5x + 6x2

Combine like terms: 1 + 35 = 36
-7X + 30x + 6xX = 36 + 5x + 6x2

Add '-30x' to each side of the equation.
-7X + 30x + -30x + 6xX = 36 + 5x + -30x + 6x2

Combine like terms: 30x + -30x = 0
-7X + 0 + 6xX = 36 + 5x + -30x + 6x2
-7X + 6xX = 36 + 5x + -30x + 6x2

Combine like terms: 5x + -30x = -25x
-7X + 6xX = 36 + -25x + 6x2

Reorder the terms:
-36 + -7X + 25x + 6xX + -6x2 = 36 + -25x + 6x2 + -36 + 25x + -6x2

Reorder the terms:
-36 + -7X + 25x + 6xX + -6x2 = 36 + -36 + -25x + 25x + 6x2 + -6x2

Combine like terms: 36 + -36 = 0
-36 + -7X + 25x + 6xX + -6x2 = 0 + -25x + 25x + 6x2 + -6x2
-36 + -7X + 25x + 6xX + -6x2 = -25x + 25x + 6x2 + -6x2

Combine like terms: -25x + 25x = 0
-36 + -7X + 25x + 6xX + -6x2 = 0 + 6x2 + -6x2
-36 + -7X + 25x + 6xX + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-36 + -7X + 25x + 6xX + -6x2 = 0

The solution to this equation could not be determined.

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