(X+1)(x+4)=(x-7)(x+6)

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Solution for (X+1)(x+4)=(x-7)(x+6) equation: 


Simplifying
(X + 1)(x + 4) = (x + -7)(x + 6)

Reorder the terms:
(1 + X)(x + 4) = (x + -7)(x + 6)

Reorder the terms:
(1 + X)(4 + x) = (x + -7)(x + 6)

Multiply (1 + X) * (4 + x)
(1(4 + x) + X(4 + x)) = (x + -7)(x + 6)
((4 * 1 + x * 1) + X(4 + x)) = (x + -7)(x + 6)
((4 + 1x) + X(4 + x)) = (x + -7)(x + 6)
(4 + 1x + (4 * X + x * X)) = (x + -7)(x + 6)
(4 + 1x + (4X + xX)) = (x + -7)(x + 6)

Reorder the terms:
(4 + 4X + 1x + xX) = (x + -7)(x + 6)
(4 + 4X + 1x + xX) = (x + -7)(x + 6)

Reorder the terms:
4 + 4X + 1x + xX = (-7 + x)(x + 6)

Reorder the terms:
4 + 4X + 1x + xX = (-7 + x)(6 + x)

Multiply (-7 + x) * (6 + x)
4 + 4X + 1x + xX = (-7(6 + x) + x(6 + x))
4 + 4X + 1x + xX = ((6 * -7 + x * -7) + x(6 + x))
4 + 4X + 1x + xX = ((-42 + -7x) + x(6 + x))
4 + 4X + 1x + xX = (-42 + -7x + (6 * x + x * x))
4 + 4X + 1x + xX = (-42 + -7x + (6x + x2))

Combine like terms: -7x + 6x = -1x
4 + 4X + 1x + xX = (-42 + -1x + x2)

Solving
4 + 4X + 1x + xX = -42 + -1x + x2

Solving for variable 'X'.

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

Add '-4' to each side of the equation.
4 + 4X + 1x + -4 + xX = -42 + -1x + -4 + x2

Reorder the terms:
4 + -4 + 4X + 1x + xX = -42 + -1x + -4 + x2

Combine like terms: 4 + -4 = 0
0 + 4X + 1x + xX = -42 + -1x + -4 + x2
4X + 1x + xX = -42 + -1x + -4 + x2

Reorder the terms:
4X + 1x + xX = -42 + -4 + -1x + x2

Combine like terms: -42 + -4 = -46
4X + 1x + xX = -46 + -1x + x2

Add '-1x' to each side of the equation.
4X + 1x + -1x + xX = -46 + -1x + -1x + x2

Combine like terms: 1x + -1x = 0
4X + 0 + xX = -46 + -1x + -1x + x2
4X + xX = -46 + -1x + -1x + x2

Combine like terms: -1x + -1x = -2x
4X + xX = -46 + -2x + x2

Reorder the terms:
46 + 4X + 2x + xX + -1x2 = -46 + -2x + x2 + 46 + 2x + -1x2

Reorder the terms:
46 + 4X + 2x + xX + -1x2 = -46 + 46 + -2x + 2x + x2 + -1x2

Combine like terms: -46 + 46 = 0
46 + 4X + 2x + xX + -1x2 = 0 + -2x + 2x + x2 + -1x2
46 + 4X + 2x + xX + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
46 + 4X + 2x + xX + -1x2 = 0 + x2 + -1x2
46 + 4X + 2x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
46 + 4X + 2x + xX + -1x2 = 0

The solution to this equation could not be determined.

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