(X+3)(x+4)=(x+7)(x-2)

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Solution for (X+3)(x+4)=(x+7)(x-2) equation: 


Simplifying
(X + 3)(x + 4) = (x + 7)(x + -2)

Reorder the terms:
(3 + X)(x + 4) = (x + 7)(x + -2)

Reorder the terms:
(3 + X)(4 + x) = (x + 7)(x + -2)

Multiply (3 + X) * (4 + x)
(3(4 + x) + X(4 + x)) = (x + 7)(x + -2)
((4 * 3 + x * 3) + X(4 + x)) = (x + 7)(x + -2)
((12 + 3x) + X(4 + x)) = (x + 7)(x + -2)
(12 + 3x + (4 * X + x * X)) = (x + 7)(x + -2)
(12 + 3x + (4X + xX)) = (x + 7)(x + -2)

Reorder the terms:
(12 + 4X + 3x + xX) = (x + 7)(x + -2)
(12 + 4X + 3x + xX) = (x + 7)(x + -2)

Reorder the terms:
12 + 4X + 3x + xX = (7 + x)(x + -2)

Reorder the terms:
12 + 4X + 3x + xX = (7 + x)(-2 + x)

Multiply (7 + x) * (-2 + x)
12 + 4X + 3x + xX = (7(-2 + x) + x(-2 + x))
12 + 4X + 3x + xX = ((-2 * 7 + x * 7) + x(-2 + x))
12 + 4X + 3x + xX = ((-14 + 7x) + x(-2 + x))
12 + 4X + 3x + xX = (-14 + 7x + (-2 * x + x * x))
12 + 4X + 3x + xX = (-14 + 7x + (-2x + x2))

Combine like terms: 7x + -2x = 5x
12 + 4X + 3x + xX = (-14 + 5x + x2)

Solving
12 + 4X + 3x + xX = -14 + 5x + x2

Solving for variable 'X'.

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

Add '-12' to each side of the equation.
12 + 4X + 3x + -12 + xX = -14 + 5x + -12 + x2

Reorder the terms:
12 + -12 + 4X + 3x + xX = -14 + 5x + -12 + x2

Combine like terms: 12 + -12 = 0
0 + 4X + 3x + xX = -14 + 5x + -12 + x2
4X + 3x + xX = -14 + 5x + -12 + x2

Reorder the terms:
4X + 3x + xX = -14 + -12 + 5x + x2

Combine like terms: -14 + -12 = -26
4X + 3x + xX = -26 + 5x + x2

Add '-3x' to each side of the equation.
4X + 3x + -3x + xX = -26 + 5x + -3x + x2

Combine like terms: 3x + -3x = 0
4X + 0 + xX = -26 + 5x + -3x + x2
4X + xX = -26 + 5x + -3x + x2

Combine like terms: 5x + -3x = 2x
4X + xX = -26 + 2x + x2

Reorder the terms:
26 + 4X + -2x + xX + -1x2 = -26 + 2x + x2 + 26 + -2x + -1x2

Reorder the terms:
26 + 4X + -2x + xX + -1x2 = -26 + 26 + 2x + -2x + x2 + -1x2

Combine like terms: -26 + 26 = 0
26 + 4X + -2x + xX + -1x2 = 0 + 2x + -2x + x2 + -1x2
26 + 4X + -2x + xX + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
26 + 4X + -2x + xX + -1x2 = 0 + x2 + -1x2
26 + 4X + -2x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
26 + 4X + -2x + xX + -1x2 = 0

The solution to this equation could not be determined.

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